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Chair Mathematics II (Computer Algebra)

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Number of items at this level: 239.

2023

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dela Cruz, Romar ; Kiermaier, Michael ; Kurz, Sascha ; Wassermann, Alfred:
On the minimum number of minimal codewords.
In: Advances in Mathematics of Communications. Vol. 17 (2023) Issue 2 . - pp. 333-341.
DOI: https://doi.org/10.3934/amc.2020130

Kiermaier, Michael ; Kurz, Sascha:
Classification of Δ-Divisible Linear Codes Spanned by Codewords of Weight Δ.
In: IEEE Transactions on Information Theory. Vol. 69 (2023) Issue 6 . - pp. 3544-3551.
DOI: https://doi.org/10.1109/TIT.2023.3239582

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Kiermaier, Michael ; Kurz, Sascha ; Solé, Patrick ; Stoll, Michael ; Wassermann, Alfred:
On strongly walk regular graphs, triple sum sets and their codes.
In: Designs, Codes and Cryptography. Vol. 91 (2023) . - pp. 645-675.
DOI: https://doi.org/10.1007/s10623-022-01118-z

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Derickx, Maarten ; Kamienny, Sheldon ; Stein, William ; Stoll, Michael:
Torsion points on elliptic curves over number fields of small degree.
In: Algebra & Number Theory. Vol. 17 (2023) Issue 2 . - pp. 267-308.
DOI: https://doi.org/10.2140/ant.2023.17.267

2022

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Kiermaier, Michael:
On α-points of q-analogs of the Fano plane.
In: Designs, Codes and Cryptography. Vol. 90 (2022) Issue 6 . - pp. 1335-1345.
DOI: https://doi.org/10.15495/EPub_UBT_00006621

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Fu, Hang ; Stoll, Michael:
Elliptic curves with common torsion x-coordinates and hyperelliptic torsion packets.
In: Proceedings of the American Mathematical Society. Vol. 150 (2022) . - pp. 5137-5149.
DOI: https://doi.org/10.1090/proc/16102
Review:

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Keller, Timo ; Stoll, Michael:
Exact verification of the strong BSD conjecture for some absolutely simple abelian surfaces.
In: Comptes Rendus Mathématique. Vol. 360 (2022) . - pp. 483-489.
DOI: https://doi.org/10.5802/crmath.313
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Reinke, Bernhard ; Schleicher, Dierk ; Stoll, Michael:
The Weierstrass–Durand–Kerner root finder is not generally convergent.
In: Mathematics of Computation. Vol. 92 (2022) Issue 340 . - pp. 839-866.
DOI: https://doi.org/10.1090/mcom/3783
Review:

2021

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Bruin, Peter ; Derickx, Maarten ; Stoll, Michael:
Elliptic curves with a point of order 13 defined over cyclic cubic fields.
In: Functiones et Approximatio Commentarii Mathematici. Vol. 65 (December 2021) Issue 2 . - pp. 191-197.
DOI: https://doi.org/10.7169/facm/1945
Review:

2020

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dela Cruz, Romar ; Kiermaier, Michael ; Kurz, Sascha ; Wassermann, Alfred:
On the minimum number of minimal codewords.
Bayreuth , 2020 . - 9 p.
DOI: https://doi.org/10.15495/EPub_UBT_00004877

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Kiermaier, Michael ; Kurz, Sascha:
On the lengths of divisible codes.
Bayreuth , 2020 . - 17 p.

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DeMark, David ; Hindes, Wade ; Jones, Rafe ; Misplon, Moses ; Stoll, Michael ; Stoneman, Michael:
Eventually stable quadratic polynomials over ℚ.
In: New York Journal of Mathematics. Vol. 26 (2020) . - pp. 526-561.

Freitas, Nuno ; Naskręcki, Bartosz ; Stoll, Michael:
The generalized Fermat equation with exponents 2, 3, n.
In: Compositio Mathematica. Vol. 156 (2020) Issue 1 . - pp. 77-113.
DOI: https://doi.org/10.1112/s0010437x19007693

Sawin, Will ; Shusterman, Mark ; Stoll, Michael:
Irreducibility of polynomials with a large gap.
In: Acta Arithmetica. Vol. 192 (2020) Issue 2 . - pp. 111-139.
DOI: https://doi.org/10.4064/aa180526-12-6

Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha ; Wassermann, Alfred:
The Lengths of Projective Triply-Even Binary Codes.
In: IEEE Transactions on Information Theory. Vol. 66 (2020) Issue 5 . - pp. 2713-2716.
DOI: https://doi.org/10.1109/TIT.2019.2940967

Kiermaier, Michael ; Kurz, Sascha:
On the lengths of divisible codes.
In: IEEE Transactions on Information Theory. Vol. 66 (2020) Issue 7 . - pp. 4051-4060.
DOI: https://doi.org/10.1109/TIT.2020.2968832

2019

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Heinlein, Daniel ; Kiermaier, Michael ; Kurz, Sascha ; Wassermann, Alfred:
Tables of subspace codes.
Bayreuth , 2019 . - 44 p.

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Kiermaier, Michael ; Kurz, Sascha ; Shi, Minjia ; Solé, Patrick:
Three-weight codes over rings and strongly walk regular graphs.
Bayreuth , 2019 . - 28 p.

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Kiermaier, Michael ; Kurz, Sascha ; Wassermann, Alfred:
Derived designs of q-Fano planes and q-analogs of group divisible designs.
2019
Event: Academy Contact Forum: Coding Theory and Cryptography VIII , 2019-09-27 , The royal Flemish academy of Belgium for science and arts, Brussels, Belgium.
(Conference item: Conference , Speech )

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Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha ; Wassermann, Alfred:
The lengths of projective triply-even binary codes.
Bayreuth , 2019 . - 6 p.

de Beule, Jan ; Kiermaier, Michael ; Kurz, Sascha ; Wassermann, Alfred:
On q-analogs of group divisible designs.
2019
Event: 9th Slovenian International Conference on Graph Theory , 23.-29.06.2019 , Bled, Slovenia.
(Conference item: Conference , Speech )

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Kiermaier, Michael ; Kurz, Sascha:
On the lengths of divisible codes.
Bayreuth , 2019 . - 17 p.

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Buratti, Marco ; Kiermaier, Michael ; Kurz, Sascha ; Nakić, Anamari ; Wassermann, Alfred:
q-analogs of group divisible designs.
Bayreuth , 2019 . - 18 p.

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Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha:
Johnson type bounds for mixed dimension subspace codes.
Bayreuth , 2019 . - 16 p.

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Heinlein, Daniel ; Kiermaier, Michael ; Kurz, Sascha ; Wassermann, Alfred:
A subspace code of size 333 in the setting of a binary q-analog of the Fano plane.
Bayreuth , 2019 . - 18 p.

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Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha:
Classification of large partial plane spreads in PG(6,2) and related combinatorial objects.
In: Journal of Geometry. Vol. 110 (2019) . - 5.
DOI: https://doi.org/10.1007/s00022-018-0459-6

Heinlein, Daniel ; Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha ; Wassermann, Alfred:
Classifying optimal binary subspace codes of length 8, constant dimension 4 and minimum distance 6.
In: Designs, Codes and Cryptography. Vol. 87 (2019) Issue 2-3 . - pp. 375-391.
DOI: https://doi.org/10.1007/s10623-018-0544-8

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Heinlein, Daniel ; Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha:
Generalized vector space partitions.
In: The Australasian Journal of Combinatorics. Vol. 73 (2019) Issue 1 . - pp. 162-178.

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Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha:
Johnson type bounds for mixed dimension subspace codes.
In: The Electronic Journal of Combinatorics. Vol. 26 (2019) Issue 3 . - P3.39.
DOI: https://doi.org/10.37236/8188

Braun, Michael ; Kiermaier, Michael ; Laue, Reinhard:
New 2-designs over finite fields from derived and residual designs.
In: Advances in Mathematics of Communications. Vol. 13 (2019) Issue 1 . - pp. 165-170.
DOI: https://doi.org/10.3934/amc.2019010

Buratti, Marco ; Kiermaier, Michael ; Kurz, Sascha ; Nakić, Anamari ; Wassermann, Alfred:
q-analogs of group divisible designs.
In: Schmidt, Kai-Uwe ; Winterhof, Arne (ed.): Combinatorics and Finite Fields : Difference Sets, Polynomials, Pseudorandomness and Applications. - Berlin : De Gruyter, 2019 . - (Radon Series on Computational and Applied Mathematics ; 23 )

Vishkautsan, Solomon ; Stoll, Michael:
Quadratic rational functions with a rational periodic critical point of period 3 : with 5 p Appendix by Michael Stoll: Rational points on a curve of genus 6.
In: Journal de Théorie des Nombres de Bordeaux. Vol. 31 (2019) Issue 1 . - pp. 49-79.
DOI: https://doi.org/10.5802/jtnb.1068

Canci, Jung Kyu ; Troncoso, Sebastian ; Vishkautsan, Solomon:
Scarcity of finite orbits for rational functions over a number field.
In: Acta Arithmetica. Vol. 190 (2019) Issue 3 . - pp. 221-237.
DOI: https://doi.org/10.4064/aa180210-4-12

Hutz, Benjamin ; Stoll, Michael:
Smallest representatives of SL(2,ℤ)-orbits of binary forms and endomorphisms of ℙ¹.
In: Acta Arithmetica. Vol. 189 (2019) Issue 3 . - pp. 283-308.
DOI: https://doi.org/10.4064/aa180618-9-12

Heinlein, Daniel ; Kiermaier, Michael ; Kurz, Sascha ; Wassermann, Alfred:
A subspace code of size 333 in the setting of a binary q-analog of the Fano plane.
In: Advances in Mathematics of Communications. Vol. 13 (2019) Issue 3 . - pp. 457-475.
DOI: https://doi.org/10.3934/amc.2019029

Stoll, Michael:
Uniform bounds for the number of rational points on hyperelliptic curves of small Mordell-Weil rank.
In: Journal of the European Mathematical Society. Vol. 21 (2019) Issue 3 . - pp. 923-956.
DOI: https://doi.org/10.4171/JEMS/857

Checcoli, Sara ; Veneziano, Francesco ; Viada, Evelina ; Stoll, Michael:
The explicit Mordell conjecture for families of curves.
In: Forum of Mathematics, Sigma. Vol. 7 (2019) . - e31.
DOI: https://doi.org/10.1017/fms.2019.20

2018

Heinlein, Daniel ; Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha ; Wassermann, Alfred:
(Multi-)Sets of subspaces and divisible codes.
2018
Event: Algebraic Coding Theory for Networks, Storage, and Security , 16-21.12.2018 , Schloß Dagstuhl, Wadern.
(Conference item: Workshop , Speech )

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Kiermaier, Michael ; Kurz, Sascha:
On the lengths of divisible codes.
2018
Event: Kolloquium über Kombinatorik (KolKom) , 23. bis 24. Nov. 2018 , Universität Paderborn.
(Conference item: Conference , Speech )

Heinlein, Daniel ; Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha ; Wassermann, Alfred:
Random Linear Network Coding - Wissenschaftliches Rechnen für den 5G-Standard?
2018
Event: Modellierung und Simulation (MODUS) , 2018 , Bayreuth.
(Conference item: Lecture series , Speech )

Kurz, Sascha ; Stoll, Michael ; Worthmann, Karl:
Angewandte Mathematik : ein Lehrbuch für Lehramtsstudierende.
Berlin : Springer , 2018 . - XVIII + 210 p.
DOI: https://doi.org/10.1007/978-3-662-56705-0

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Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha:
Classification of large partial plane spreads in PG(6,2) and related combinatorial objects.
Bayreuth , 2018 . - 31 p.

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Heinlein, Daniel ; Kiermaier, Michael ; Kurz, Sascha ; Wassermann, Alfred:
Tables of Subspacecodes.
2018
Event: Munich Workshop on Coding and Cryptography 2018 , 10.-11.04.2018 , München.
(Conference item: Workshop , Poster )

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Heinlein, Daniel ; Kiermaier, Michael ; Kurz, Sascha ; Wassermann, Alfred:
q-Analoga von Designs, Subspace Codes und verwandte Objekte.
2018
Event: Gemeinsame Jahrestagung GDMV 2018 , 05.-09.03.2018 , Paderborn.
(Conference item: Conference , Speech )

Wassermann, Alfred ; Buratti, Marco ; Kurz, Sascha ; Nakić, Anamari ; Kiermaier, Michael:
q-analogs of group divisible designs.
2018
Event: Discretaly: A Workshop in Discrete Mathematics , 1.-2.2.2018 , Rome, Italy.
(Conference item: Workshop , Speech )

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Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha:
Partial Spreads and Vector Space Partitions.
In: Greferath, Marcus ; Pavčević, Mario Osvin ; Silberstein, Natalia ; Vázquez-Castro, María Ángeles (ed.): Network Coding and Subspace Designs. - Cham : Springer, 2018 . - pp. 131-170 . - (Signals and Communication Technology )
DOI: https://doi.org/10.1007/978-3-319-70293-3_7

Braun, Michael ; Kiermaier, Michael ; Wassermann, Alfred:
Computational methods in subspace designs.
In: Greferath, Marcus ; Pavčević, Mario Osvin ; Natalia, Silberstein ; María Ángeles, Vázquez-Castro (ed.): Network Coding and Subspace Designs. - Cham : Springer, 2018 . - pp. 213-244 . - (Signals and Communication Technology )
DOI: https://doi.org/10.1007/978-3-319-70293-3_9

Keller, Timo:
A duality theorem for Tate–Shafarevich groups of curves over algebraically closed fields.
In: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg. Vol. 88 (2018) Issue 2 . - pp. 289-295.
DOI: https://doi.org/10.1007/s12188-018-0196-7

Kiermaier, Michael ; Laue, Reinhard ; Wassermann, Alfred:
A new series of large sets of subspace designs over the binary field.
In: Designs, Codes and Cryptography. Vol. 86 (2018) Issue 2 . - pp. 251-268.
DOI: https://doi.org/10.1007/s10623-017-0349-1

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Kiermaier, Michael ; Kurz, Sascha ; Wassermann, Alfred:
The order of the automorphism group of a binary q-analog of the Fano plane is at most two.
In: Designs, Codes and Cryptography. Vol. 86 (2018) Issue 2 . - pp. 239-250.
DOI: https://doi.org/10.1007/s10623-017-0360-6

Braun, Michael ; Kiermaier, Michael ; Wassermann, Alfred:
q-analogs of designs : Subspace designs.
In: Greferath, Marcus ; Pavčević, Mario Osvin ; Silberstein, Natalia ; Vázquez-Castro, María Ángeles (ed.): Network Coding and Subspace Designs. - Cham : Springer, 2018 . - pp. 171-211 . - (Signals and Communication Technology )
DOI: https://doi.org/10.1007/978-3-319-70293-3_8

2017

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Heinlein, Daniel ; Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha ; Wassermann, Alfred:
Classifying optimal binary subspace codes of length 8, constant dimension 4 and minimum distance 6.
Bayreuth , 2017 . - 16 p.

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Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha:
Partial spreads and vector space partitions.
Bayreuth , 2017 . - 30 p.

Stoll, Michael:
Chabauty without the Mordell-Weil group.
In: Böckle, Gebhard ; Decker, Wolfram ; Malle, Gunter (ed.): Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory. - Cham : Springer, 2017 . - pp. 623-663
DOI: https://doi.org/10.1007/978-3-319-70566-8_28

Stoll, Michael:
An explicit theory of heights for hyperelliptic Jacobians of genus three.
In: Böckle, Gebhard ; Decker, Wolfram ; Malle, Gunter (ed.): Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory. - Cham : Springer, 2017 . - pp. 665-715
DOI: https://doi.org/10.1007/978-3-319-70566-8_29

Bauer, Ingrid ; Stoll, Michael:
Geometry and arithmetic of primary Burniat surfaces.
In: Mathematische Nachrichten. Vol. 290 (2017) Issue 14–15 . - pp. 2132-2153.
DOI: https://doi.org/10.1002/mana.201600282
Review:

Braun, Michael ; Kiermaier, Michael ; Kohnert, Axel ; Laue, Reinhard:
Large sets of subspace designs.
In: Journal of Combinatorial Theory, Series A. Vol. 147 (2017) . - pp. 155-185.
DOI: https://doi.org/10.1016/j.jcta.2016.11.004

Kühn, Ulf ; Müller, Jan Steffen:
Lower bounds on the arithmetic self-intersection number of the relative dualizing sheaf on arithmetic surfaces.
In: Transactions of the American Mathematical Society. Vol. 369 (2017) Issue 3 . - pp. 1869-1894.
DOI: https://doi.org/10.1090/tran/6787

Heinlein, Daniel ; Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha ; Wassermann, Alfred:
Projective divisible binary codes.
In: Augot, Daniel ; Krouk, Evgeny ; Loidreau, Pierre (ed.): The Tenth International Workshop on Coding and Cryptography 2017 : WCC Proceedings. - Saint-Petersburg , 2017

Stoll, Michael:
Simultaneous torsion in the Legendre family.
In: Experimental Mathematics. Vol. 26 (2017) Issue 4 . - pp. 446-459.
DOI: https://doi.org/10.1080/10586458.2016.1201443

2016

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Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha:
Constructions and Bounds for Mixed-Dimension Subspace Codes.
Bayreuth , 2016 . - 35 p.

Heinlein, Daniel ; Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha ; Wassermann, Alfred:
Subspace codes.
2016
Event: Workshop in coding theory and cryptography , 21.11.2016 , Brussels.
(Conference item: Workshop , Speech )

de la Cruz, Javier ; Kiermaier, Michael ; Wassermann, Alfred ; Willems, Wolfgang:
Algebraic structures of MRD codes.
In: Advances in Mathematics of Communications. Vol. 10 (2016) Issue 3 . - pp. 499-510.
DOI: https://doi.org/10.3934/amc.2016021

de la Cruz, Javier ; Kiermaier, Michael ; Wassermann, Alfred:
The automorphism group of an extremal [120, 60, 24] code does not contain elements of order 29.
In: Designs, Codes and Cryptography. Vol. 78 (2016) Issue 3 . - pp. 693-702.
DOI: https://doi.org/10.1007/s10623-014-0025-7

Müller, Jan Steffen ; Stoll, Michael:
Canonical heights on genus-2 Jacobians.
In: Algebra & Number Theory. Vol. 10 (2016) Issue 10 . - pp. 2153-2234.
DOI: https://doi.org/10.2140/ant.2016.10.2153

Müller, Jan Steffen ; Stoll, Michael:
Computing canonical heights on elliptic curves in quasi-linear time.
In: LMS Journal of Computation and Mathematics. Vol. 19 (2016) . - pp. 391-405.
DOI: https://doi.org/10.1112/S1461157016000139

Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha:
Constructions and bounds for mixed-dimension subspace codes.
In: Advances in Mathematics of Communications. Vol. 10 (2016) Issue 3 . - pp. 649-682.
DOI: https://doi.org/10.3934/amc.2016033

Kerber, Adalbert ; Kiermaier, Michael ; Laue, Reinhard ; Pavčević, Mario Osvin ; Wassermann, Alfred:
Editorial.
In: Advances in Mathematics of Communications. Vol. 10 (2016) Issue 3 . - S. I-II.
DOI: https://doi.org/10.3934/amc.201603i

Bruin, Nils ; Poonen, Bjorn ; Stoll, Michael:
Generalized explicit descent and its application to curves of genus 3.
In: Forum of Mathematics, Sigma. Vol. 4 (2016) . - e6.
DOI: https://doi.org/10.1017/fms.2016.1

Kiermaier, Michael ; Wassermann, Alfred ; Zwanzger, Johannes:
New upper bounds on binary linear codes and a ℤ₄-code with a better-than-linear Gray image.
In: IEEE Transactions on Information Theory. Vol. 62 (2016) Issue 12 . - pp. 6768-6771.
DOI: https://doi.org/10.1109/TIT.2016.2612654

Honold, Thomas ; Kiermaier, Michael:
On putative q-analogues of the Fano plane and related combinatorial structures.
In: Hagen, Thomas ; Rupp, Florian ; Scheurle, Jürgen (ed.): Dynamical Systems, Number Theory and Applications : A Festschrift in Honor of Armin Leutbecher’s 80th Birthday. - New Jersey : World Scientific, 2016 . - pp. 141-175
DOI: https://doi.org/10.1142/9789814699877_0008

Braun, Michael ; Kiermaier, Michael ; Nakić, Anamari:
On the automorphism group of a binary q-analog of the Fano plane.
In: European Journal of Combinatorics. Vol. 51 (2016) . - pp. 443-457.
DOI: https://doi.org/10.1016/j.ejc.2015.07.014

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Kiermaier, Michael ; Kurz, Sascha ; Wassermann, Alfred:
The order of the automorphism group of a binary q-analog of the Fano plane is at most two.
Bayreuth , 2016 . - 10 p.

Balakrishnan, Jennifer S. ; Müller, Jan Steffen ; Stein, William A.:
A p-adic analogue of the conjecture of Birch and Swinnerton-Dyer for modular abelian varieties.
In: Mathematics of Computation. Vol. 85 (2016) Issue 298 . - pp. 983-1016.
DOI: https://doi.org/10.1090/mcom/3029

Balakrishnan, Jennifer S. ; Besser, Amnon ; Müller, Jan Steffen:
Quadratic Chabauty : p-adic heights and integral points on hyperelliptic curves.
In: Journal für die Reine und Angewandte Mathematik. (2016) Issue 720 . - pp. 51-79.
DOI: https://doi.org/10.1515/crelle-2014-0048

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Schmidt, Miriam:
Rank metric codes.
Bayreuth , 2016 . - VI, 67 p.
(Master's, 2016 , Universität Bayreuth, Fakultät für Mathematik, Physik und Informatik, Lehrstuhl Mathematik II)

2015

Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha:
Improved bounds and classification results for binary subspace codes.
2015
Event: 7th Workshop on Coding and Systems , 01.-03.07.2015 , Salamanca, Spain.
(Conference item: Workshop , Speech )

Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha:
ILP techniques for binary subspace codes.
2015
Event: Algebraic combinatorics and applications - ALCOMA 2015 , 15.-20.03.2015 , Kloster Banz, Germany.
(Conference item: Conference , Speech )

ALCOMA 15 : Algebraic Combinatorics and Applications.
ed.: Kerber, Adalbert ; Kiermaier, Michael ; Laue, Reinhard ; Pavčević, Mario Osvin ; Wassermann, Alfred

Bayreuth , 2015 . - 84 p.

Freitas, Nuno ; Siksek, Samir:
The asymptotic Fermat's last theorem for five-sixths of real quadratic fields.
In: Compositio Mathematica. Vol. 151 (2015) Issue 8 . - pp. 1395-1415.
DOI: https://doi.org/10.1112/S0010437X14007957

Freitas, Nuno ; Siksek, Samir:
Criteria for irreducibility of mod p representations of Frey curves.
In: Journal de Théorie des Nombres de Bordeaux. Vol. 27 (2015) Issue 1 . - pp. 67-76.
DOI: https://doi.org/10.5802/jtnb.894

Kiermaier, Michael ; Laue, Reinhard:
Derived and residual subspace designs.
In: Advances in Mathematics of Communications. Vol. 9 (2015) Issue 1 . - pp. 105-115.
DOI: https://doi.org/10.3934/amc.2015.9.105

Stoll, Michael:
Descent and covering collections.
In: Beshaj, Lubjana ; Shaska, Tony ; Zhupa, Eustrat ; NATO (ed.): Advances on superelliptic curves and their applications : Including papers based on the NATO Advanced Study Institute (ASI) on Hyperelliptic Curve Cryptography held in Ohrid, August 25-September 5, 2014. - Amsterdam : IOS Press, 2015 . - pp. 176-193 . - (NATO Science for Peace and Security : Series D, Information and Communication Security ; 41 )
DOI: https://doi.org/10.3233/978-1-61499-520-3-176

Freitas, Nuno ; Le Hung, Bao V. ; Siksek, Samir:
Elliptic curves over real quadratic fields are modular.
In: Inventiones Mathematicae. Vol. 201 (2015) Issue 1 . - pp. 159-206.
DOI: https://doi.org/10.1007/s00222-014-0550-z

Cremona, John E. ; Fisher, Tom A. ; O'Neil, C. ; Simon, D. ; Stoll, Michael:
Explicit n-descent on elliptic curves III. Algorithms.
In: Mathematics of Computation. Vol. 84 (2015) Issue 292 . - pp. 895-922.
DOI: https://doi.org/10.1090/S0025-5718-2014-02858-5

Freitas, Nuno ; Siksek, Samir:
Fermat’s last theorem over some small real quadratic fields.
In: Algebra & Number Theory. Vol. 9 (2015) Issue 4 . - pp. 875-895.
DOI: https://doi.org/10.2140/ant.2015.9.875

Kühn, Ulf ; Müller, Jan Steffen:
A height inequality for rational points on elliptic curves implied by the abc-conjecture.
In: Functiones et Approximatio Commentarii Mathematici. Vol. 52 (2015) Issue 1 . - pp. 127-132.
DOI: https://doi.org/10.7169/facm/2015.52.1.10

Kiermaier, Michael ; Pavčević, Mario Osvin:
Intersection numbers for subspace designs.
In: Journal of Combinatorial Designs. Vol. 23 (2015) Issue 11 . - pp. 463-480.
DOI: https://doi.org/10.1002/jcd.21403

Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha:
Optimal binary subspace codes of length 6, constant dimension 3 and minimum subspace distance 4.
In: Kyureghyan, Gohar ; Mullen, Gary L. ; Pott, Alexander (Hrsg.): Topics in Finite Fields. - Providence, Rhode Island : American Mathematical Society, 2015 . - pp. 157-176 . - (Contemporary Mathematics ; 632 )
DOI: https://doi.org/10.1090/conm/632/12627

Freitas, Nuno:
Recipes to Fermat-type equations of the form xʳ+yʳ=Czᵖ.
In: Mathematische Zeitschrift. Vol. 279 (2015) . - pp. 605-639.
DOI: https://doi.org/10.1007/s00209-014-1384-5

2014

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Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha:
Optimal binary subspace codes of length 6, constant dimension 3 and minimum distance 4.
Bayreuth , 2014 . - 24 p.

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Matev, Tzanko:
Good reduction of 1-motives.
Bayreuth , 2014 . - IX, 115 p.
( Doctoral thesis, 2013 , Universität Bayreuth, Fakultät für Mathematik, Physik und Informatik)

Volltext
Feulner, Thomas:
Eine kanonische Form zur Darstellung äquivalenter Codes : Computergestützte Berechnung und ihre Anwendung in der Codierungstheorie, Kryptographie und Geometrie.
Bayreuth , 2014 . - IX, 176 p.
( Doctoral thesis, 2013 , Universität Bayreuth, Fakultät für Mathematik, Physik und Informatik)

Volltext
Feulner, Thomas:
Classification and nonexistence results for linear codes with prescribed minimum distances.
In: Designs, Codes and Cryptography. Vol. 70 (2014) Issue 1-2 . - pp. 127-138.
DOI: https://doi.org/10.1007/s10623-012-9700-8

Siksek, Samir ; Stoll, Michael:
The generalised Fermat equation x²+y³=z¹⁵.
In: Archiv der Mathematik. Vol. 102 (2014) . - pp. 411-421.
DOI: https://doi.org/10.1007/s00013-014-0639-z

Carlet, Claude ; Freibert, Finley ; Guilley, Sylvain ; Kiermaier, Michael ; Kim, Jon-Lark ; Solé, Patrick:
Higher-order CIS codes.
In: IEEE Transactions on Information Theory. Vol. 60 (2014) Issue 9 . - pp. 5283-5295.
DOI: https://doi.org/10.1109/TIT.2014.2332468

Braun, Michael ; Kohnert, Axel ; Östergård, Patric R. J. ; Wassermann, Alfred:
Large sets of t-designs over finite fields.
In: Journal of Combinatorial Theory, Series A. Vol. 124 (2014) . - pp. 195-202.
DOI: https://doi.org/10.1016/j.jcta.2014.01.008

Poonen, Bjorn ; Stoll, Michael:
Most odd degree hyperelliptic curves have only one rational point.
In: Annals of Mathematics. Vol. 180 (2014) Issue 3 . - pp. 1137-1166.
DOI: https://doi.org/10.4007/annals.2014.180.3.7

Greenberg, Ralph ; Rubin, Karl ; Silverberg, Alice ; Stoll, Michael:
On elliptic curves with an isogeny of degree 7.
In: American Journal of Mathematics. Vol. 136 (2014) Issue 1 . - pp. 77-109.
DOI: https://doi.org/10.1353/ajm.2014.0005

Volltext
Braun, Michael ; Kiermaier, Michael ; Nakić, Anamari:
On the automorphism group of the binary q-analog of the Fano plane.
In: Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems : MTNS 2014. - Groningen : Univ., 2014 . - pp. 1402-1405

Derenthal, Ulrich ; Elsenhans, Andreas-Stephan ; Jahnel, Jörg:
On the factor alpha in Peyre’s constant.
In: Mathematics of Computation. Vol. 83 (2014) Issue 286 . - pp. 965-977.
DOI: https://doi.org/10.1090/S0025-5718-2013-02772-X

Volltext
Stoll, Michael:
Rational points on hyperelliptic curves : recent developments.
In: Computeralgebra-Rundbrief. Vol. 54 (2014) . - pp. 10-13.

Creutz, Brendan:
Second p-descents on elliptic curves.
In: Mathematics of Computation. Vol. 83 (2014) Issue 285 . - pp. 365-409.
DOI: https://doi.org/10.1090/S0025-5718-2013-02713-5

2013

Kiermaier, Michael:
Codes from translation schemes on Galois rings of characteristic 4.
In: Electronic Notes in Discrete Mathematics. Vol. 40 (2013) . - pp. 175-180.
DOI: https://doi.org/10.1016/j.endm.2013.05.032

Honold, Thomas ; Kiermaier, Michael:
The existence of maximal (q², 2)-arcs in projective Hjelmslev planes over chain rings of length 2 and odd prime characteristic.
In: Designs, Codes and Cryptography. Vol. 68 (2013) Issue 1–3 . - pp. 105-126.
DOI: https://doi.org/10.1007/s10623-012-9653-y

Volltext
Elsenhans, Andreas-Stephan ; Jahnel, Jörg:
Experiments with the transcendental Brauer-Manin obstruction.
In: Howe, Everett W. ; Kedlaya, Kiran S. (Hrsg.): ANTS X : Proceedings. - Berkeley, CA : Mathematical Sciences Publishers, 2013 . - pp. 369-394 . - (The Open Book Series ; 1 )
DOI: https://doi.org/10.2140/obs.2013.1.369

Miller, Robert L. ; Stoll, Michael:
Explicit isogeny descent on elliptic curves.
In: Mathematics of Computation. Vol. 82 (2013) . - pp. 513-529.
DOI: https://doi.org/10.1090/S0025-5718-2012-02619-6

Volltext
Stoll, Michael ; van Luijk, Ronald:
Explicit Selmer groups for cyclic covers of P¹.
In: Acta Arithmetica. Vol. 159 (2013) . - pp. 133-148.
DOI: https://doi.org/10.4064/aa159-2-4

Kiermaier, Michael ; Zwanzger, Johannes:
New ring-linear codes from dualization in projective Hjelmslev geometries.
In: Designs, Codes and Cryptography. Vol. 66 (2013) Issue 1–3 . - pp. 39-55.
DOI: https://doi.org/10.1007/s10623-012-9650-1

Elsenhans, Andreas-Stephan ; Jahnel, Jörg:
On the computation of the Picard group for certain singular quartic surfaces.
In: Mathematica Slovaca. Vol. 63 (2013) Issue 2 . - pp. 215-228.
DOI: https://doi.org/10.2478/s12175-012-0094-x

Kiermaier, Michael:
There is no self-dual ℤ₄-linear code whose Gray image has the parameters (72,2³⁶,16).
In: IEEE Transactions on Information Theory. Vol. 59 (2013) Issue 6 . - pp. 3384-3386.
DOI: https://doi.org/10.1109/TIT.2013.2246816

Volltext
Feulner, Thomas ; Sok, Lin ; Solé, Patrick ; Wassermann, Alfred:
Towards the classification of self-dual bent functions in eight variables.
In: Designs, Codes and Cryptography. Vol. 68 (2013) Issue 1–3 . - pp. 395-406.
DOI: https://doi.org/10.1007/s10623-012-9740-0

2012

Volltext
Feulner, Thomas ; Nebe, Gabriele:
The automorphism group of an extremal [72,36,16] code does not contain Z₇, Z₃ x Z₃, or D₁₀.
In: IEEE Transactions on Information Theory. Vol. 58 (2012) Issue 11 . - pp. 6916-6924.
DOI: https://doi.org/10.1109/TIT.2012.2208176

Stoll, Michael:
Descent on elliptic curves.
In: Belabas, Karim ; Beukers, Frits ; Gaudry, Pierrick ; McCallum, William ; Poonen, Bjorn ; Siksek, Samir ; Stoll, Michael ; Watkins, Mark (ed.): Explicit methods in number theory : Rational points & Diophantine equations. Lectures from the Special Trimester held at the Institut Henri Poincaré, Paris, September–December 2004. - Paris : Société Mathématique de France, 2012 . - pp. 51-80 . - (Panoramas et Synthèses ; 36 )

Kiermaier, Michael ; Landjev, Ivan:
Designs in projective Hjelmslev spaces.
In: Lavrauw, Michel (Hrsg.): Theory and Applications of Finite Fields. - Providence, RI : American Mathematical Society, 2012 . - pp. 111-121 . - (Contemporary Mathematics ; 579 )
DOI: https://doi.org/10.1090/conm/579/11524

Elsenhans, Andreas-Stephan ; Jahnel, Jörg:
The discriminant of a cubic surface.
In: Geometriae Dedicata. Vol. 159 (2012) Issue 1 . - pp. 29-40.
DOI: https://doi.org/10.1007/s10711-011-9643-7

Volltext
Kiermaier, Michael:
Geometrische Konstruktionen linearer Codes über Galois-Ringen der Charakteristik 4 von hoher homogener Minimaldistanz.
Bayreuth , 2012 . - IV, 95 p.
( Doctoral thesis, 2012 , Universität Bayreuth, Fakultät für Mathematik, Physik und Informatik)

Elsenhans, Andreas-Stephan:
Invariants for the computation of intransitive and transitive Galois groups.
In: Journal of Symbolic Computation. Vol. 47 (2012) Issue 3 . - pp. 315-326.
DOI: https://doi.org/10.1016/j.jsc.2011.11.006

Elsenhans, Andreas-Stephan ; Jahnel, Jörg:
Kummer surfaces and the computation of the Picard group.
In: LMS Journal of Computation and Mathematics. Vol. 15 (2012) . - pp. 84-100.
DOI: https://doi.org/10.1112/S1461157012000022

Busch, Vincenz ; Müller, Jan Steffen:
Local heights on elliptic curves and intersection multiplicities.
In: International Journal of Number Theory. Vol. 8 (2012) Issue 6 . - pp. 1477-1484.
DOI: https://doi.org/10.1142/S179304211250087X

Honold, Thomas ; Kiermaier, Michael:
The maximal size of 6- and 7-arcs in projective Hjelmslev planes over chain rings of order 9.
In: Science China Mathematics. Vol. 55 (2012) Issue 1 . - pp. 73-92.
DOI: https://doi.org/10.1007/s11425-011-4296-4

Kiermaier, Michael ; Wassermann, Alfred:
Minimum weights and weight enumerators of ℤ₄-linear quadratic residue codes.
In: IEEE Transactions on Information Theory. Vol. 58 (2012) Issue 7 . - pp. 4870-4883.
DOI: https://doi.org/10.1109/TIT.2012.2191389

Nedden, Max:
Neue Methoden zur Charakterisierung der QSAR-Anwendungsdomäne : Modifizierte Kerndichteschätzung der Vorhersagegüte empirisch abgeleiteter Modelle in der Chemie.
Berlin : Springer , 2012 . - XVI, 531 p. - (Springer Research )
( Doctoral thesis, 2012 , Universität Bayreuth, Fakultät für Mathematik, Physik und Informatik)

Elsenhans, Andreas-Stephan ; Jahnel, Jörg:
On cubic surfaces with a rational line.
In: Archiv der Mathematik. Vol. 98 (2012) . - pp. 229-234.
DOI: https://doi.org/10.1007/s00013-012-0356-4

Elsenhans, Andreas-Stephan ; Jahnel, Jörg:
On the arithmetic of the discriminant for cubic surfaces.
In: Journal of the Ramanujan Mathematical Society. Vol. 27 (2012) Issue 3 . - pp. 355-373.

Elsenhans, Andreas-Stephan ; Jahnel, Jörg:
On the order three Brauer classes for cubic surfaces.
In: Central European Journal of Mathematics. Vol. 10 (2012) . - pp. 903-926.
DOI: https://doi.org/10.2478/s11533-012-0042-6

Elsenhans, Andreas-Stephan ; Jahnel, Jörg:
On the quasi-group of a cubic surface over a finite field.
In: Journal of Number Theory. Vol. 132 (2012) Issue 7 . - pp. 1554-1571.
DOI: https://doi.org/10.1016/j.jnt.2012.01.010

Volltext
Siksek, Samir ; Stoll, Michael:
Partial descent on hyperelliptic curves and the generalized Fermat equation x³+y⁴+z⁵=0.
In: The Bulletin of the London Mathematical Society. Vol. 44 (2012) Issue 1 . - pp. 151-166.
DOI: https://doi.org/10.1112/blms/bdr086

Byrne, Eimear ; Kiermaier, Michael ; Sneyd, Alison:
Properties of codes with two homogeneous weights.
In: Finite Fields and their Applications. Vol. 18 (2012) Issue 4 . - pp. 711-727.
DOI: https://doi.org/10.1016/j.ffa.2012.01.002

Elsenhans, Andreas-Stephan:
Rational points on diagonal quartic surfaces.
In: Mathematics of Computation. Vol. 81 (2012) Issue 277 . - pp. 481-492.
DOI: https://doi.org/10.1090/S0025-5718-2011-02500-7

Volltext
Geigant, Edith ; Stoll, Michael:
Stability of peak solutions of a non-linear transport equation on the circle.
In: Electronic Journal of Differential Equations. Vol. 2012 (2012) Issue 157 . - pp. 1-41.

2011

Volltext
Kiermaier, Michael ; Zwanzger, Johannes:
New ring-linear codes from geometric dualization.
In: Augot, Daniel (Hrsg.): WCC 2011 : Proceedings of the Seventh International Workshop on Coding and Cryptography. - Paris : inventeurs du monde numérique (Inria), 2011 . - pp. 111-120

Kiermaier, Michael ; Koch, Matthias ; Kurz, Sascha:
2-arcs of maximal size in the affine and the projective Hjelmslev plane over Z25.
In: Advances in Mathematics of Communications. Vol. 5 (2011) Issue 2 . - pp. 287-301.
DOI: https://doi.org/10.3934/amc.2011.5.287

Feulner, Thomas:
Canonization of linear codes over ℤ₄.
In: Advances in Mathematics of Communications. Vol. 5 (2011) Issue 2 . - pp. 245-266.
DOI: https://doi.org/10.3934/amc.2011.5.245

Volltext
Elsenhans, Andreas-Stephan ; Jahnel, Jörg:
Cubic surfaces with a Galois invariant pair of Steiner trihedra.
In: International Journal of Number Theory. Vol. 7 (2011) Issue 4 . - pp. 947-970.
DOI: https://doi.org/10.1142/S1793042111004253

Stoll, Michael:
How to Solve a Diophantine Equation.
In: Schleicher, Dierk ; Lackmann, Malte (Hrsg.): An Invitation to Mathematics : From Competitions to Research. - Heidelberg ; Dordrecht ; London ; New York : Springer, 2011 . - pp. 9-19
DOI: https://doi.org/10.1007/978-3-642-19533-4_2

Kiermaier, Michael ; Zwanzger, Johannes:
A ℤ₄-linear code of high minimum Lee distance derived from a hyperoval.
In: Advances in Mathematics of Communications. Vol. 5 (2011) Issue 2 . - pp. 275-286.
DOI: https://doi.org/10.3934/amc.2011.5.275

Volltext
Elsenhans, Andreas-Stephan ; Jahnel, Jörg:
On the computation of the Picard group for K3 surfaces.
In: Mathematical Proceedings of the Cambridge Philosophical Society. Vol. 151 (2011) Issue 2 . - pp. 263-270.
DOI: https://doi.org/10.1017/S0305004111000326

Volltext
Faber, Xander ; Hutz, Benjamin ; Stoll, Michael:
On the number of rational iterated preimages of the origin under quadratic dynamical systems.
In: International Journal of Number Theory. Vol. 7 (2011) Issue 7 . - pp. 1781-1806.
DOI: https://doi.org/10.1142/S1793042111004162

Elsenhans, Andreas-Stephan ; Jahnel, Jörg:
The Picard group of a K3 surface and its reduction modulo p.
In: Algebra & Number Theory. Vol. 5 (2011) Issue 8 . - pp. 1027-1040.
DOI: https://doi.org/10.2140/ant.2011.5.1027

Stoll, Michael:
Rational points on curves.
In: Journal de Théorie des Nombres de Bordeaux. Vol. 23 (2011) Issue 1 . - pp. 257-277.
DOI: https://doi.org/10.5802/jtnb.760

Volltext
Elsenhans, Andreas-Stephan:
Rational points on some Fano quadratic bundles.
In: Experimental Mathematics. Vol. 20 (2011) Issue 4 . - pp. 373-379.
DOI: https://doi.org/10.1080/10586458.2011.565254

Volltext
Stoll, Michael:
Reduction theory of point clusters in projective space.
In: Groups, Geometry, and Dynamics. Vol. 5 (2011) Issue 2 . - pp. 553-565.
DOI: https://doi.org/10.4171/GGD/139

2010

Volltext
Creutz, Brendan:
Explicit second p-descent on elliptic curves.
2010
( Doctoral thesis, 2010 , Jacobs University Bremen)

Elsenhans, Andreas-Stephan ; Jahnel, Jörg:
Cubic surfaces with a Galois invariant double-six.
In: Central European Journal of Mathematics. Vol. 8 (2010) Issue 4 . - pp. 646-661.
DOI: https://doi.org/10.2478/s11533-010-0036-1

Müller, Jan Steffen:
Explicit Kummer surface formulas for arbitrary characteristic.
In: LMS Journal of Computation and Mathematics. Vol. 13 (2010) . - pp. 47-64.
DOI: https://doi.org/10.1112/S1461157008000156

Cremona, John E. ; Fisher, Tom A. ; Stoll, Michael:
Minimisation and reduction of 2-, 3- and 4-coverings of elliptic curves.
In: Algebra & Number Theory. Vol. 4 (2010) Issue 6 . - pp. 763-820.
DOI: https://doi.org/10.2140/ant.2010.4.763

Bruin, Nils ; Stoll, Michael:
The Mordell-Weil sieve : proving non-existence of rational points on curves.
In: LMS Journal of Computation and Mathematics. Vol. 13 (2010) . - pp. 272-306.
DOI: https://doi.org/10.1112/S1461157009000187

Volltext
Honold, Thomas ; Kiermaier, Michael ; Landjev, Ivan:
New arcs of maximal size in projective Hjelmslev planes of order 9.
In: Comptes Rendus de l'Académie Bulgare des Sciences. Vol. 63 (2010) Issue 2 . - pp. 171-180.

Volltext
Harada, Masaaki ; Kiermaier, Michael ; Wassermann, Alfred ; Yorgova, Radinka:
New binary singly even self-dual codes.
In: IEEE Transactions on Information Theory. Vol. 56 (2010) Issue 4 . - pp. 1612-1617.
DOI: https://doi.org/10.1109/TIT.2010.2040967
Review:

Byrne, Eimear ; Greferath, Marcus ; Kohnert, Axel ; Skachek, Vitaly:
New bounds for codes over finite Frobenius rings.
In: Designs, Codes and Cryptography. Vol. 57 (2010) . - pp. 169-179.
DOI: https://doi.org/10.1007/s10623-009-9359-y

Kiermaier, Michael ; Zwanzger, Johannes:
A new series of ℤ₄-linear codes of high minimum Lee distance derived from the Kerdock codes.
In: Edelmayer, András (Hrsg.): Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems. - Budapest , 2010 . - pp. 929-932

Siksek, Samir ; Stoll, Michael:
On a problem of Hajdu and Tengely.
In: Hanrot, Guillaume ; Morain, Francois ; Thomé, Emmanuel (Hrsg.): Algorithmic Number Theory : 9th international symposium, ANTS-IX, Nancy, France, July 19-23, 2010, proceedings. - Heidelberg : Springer, 2010 . - pp. 316-330 . - (Lecture Notes in Computer Science ; 6197 )
DOI: https://doi.org/10.1007/978-3-642-14518-6_25

Elsenhans, Andreas-Stephan ; Jahnel, Jörg:
On the Brauer-Manin obstruction for cubic surfaces.
In: Journal of Combinatorics and Number Theory. Vol. 2 (2010) Issue 2 . - pp. 107-128.

Fisher, Tom A. ; Schaefer, Edward F. ; Stoll, Michael:
The yoga of the Cassels-Tate pairing.
In: LMS Journal of Computation and Mathematics. Vol. 13 (2010) . - pp. 451-460.
DOI: https://doi.org/10.1112/S1461157010000185

2009

Volltext
Stoll, Michael:
Rational Points on Curves of Genus 2 : Experiments and Speculations.
In: Johannes A. Buchmann, John Cremona and Michael E. Pohst (editors): Algorithms and Number Theory. - Wadern , 2009 . - 4 S . - (Dagstuhl Seminar Proceedings ; 09221 )

Feulner, Thomas:
The automorphism groups of linear codes and canonical representatives of their semilinear isometry classes.
In: Advances in Mathematics of Communications. Vol. 3 (2009) Issue 4 . - pp. 363-383.
DOI: https://doi.org/10.3934/amc.2009.3.363

Kohnert, Axel ; Wassermann, Alfred:
Construction of binary and ternary self-orthogonal linear codes.
In: Discrete Applied Mathematics. Vol. 157 (2009) Issue 9 . - pp. 2118-2123.
DOI: https://doi.org/10.1016/j.dam.2007.10.030
Review:

Cremona, John E. ; Fisher, Tom A. ; O'Neil, C. ; Simon, D. ; Stoll, Michael:
Explicit n-descent on elliptic curves, II. Geometry.
In: Journal für die Reine und Angewandte Mathematik. (2009) Issue 632 . - pp. 63-84.
DOI: https://doi.org/10.1515/CRELLE.2009.050

Volltext
Kohnert, Axel ; Kurz, Sascha:
Integral point sets over Z_n^m.
In: Discrete Applied Mathematics. Vol. 157 (2009) Issue 9 . - pp. 2105-2117.
DOI: https://doi.org/10.1016/j.dam.2007.10.019

Kohnert, Axel:
(l, s)-extension of linear codes.
In: Discrete Mathematics. Vol. 309 (2009) Issue 2 . - pp. 412-417.
DOI: https://doi.org/10.1016/j.disc.2007.12.028

Volltext
Kiermaier, Michael ; Kurz, Sascha:
Maximal integral point sets in affine planes over finite fields.
In: Discrete Mathematics. Vol. 309 (2009) Issue 13 . - pp. 4564-4575.
DOI: https://doi.org/10.1016/j.disc.2009.02.020

Kohnert, Axel ; Zwanzger, Johannes:
New linear codes with prescribed group of automorphisms found by heuristic search.
In: Advances in Mathematics of Communications. Vol. 3 (2009) Issue 2 . - pp. 157-166.
DOI: https://doi.org/10.3934/amc.2009.3.157

Volltext
Elsenhans, Andreas-Stephan ; Jahnel, Jörg:
New sums of three cubes.
In: Mathematics of Computation. Vol. 78 (2009) Issue 266 . - pp. 1227-1230.
DOI: https://doi.org/10.1090/S0025-5718-08-02168-6

Stoll, Michael ; Walsh, P. G. ; Yuan, Pingzhi:
On the Diophantine equation X² - (2²ᵐ + 1) Y⁴ = -2²ᵐ.
In: Acta Arithmetica. Vol. 139 (2009) Issue 1 . - pp. 57-63.
DOI: https://doi.org/10.4064/aa139-1-5

Volltext
Byrne, Eimear ; Greferath, Marcus ; Kohnert, Axel ; Skachek, Vitaly:
Refined bounds for ring-linear codes.
In: International Workshop on Optimal Codes and Related Topics : proceedings. - Varna, Bulgaria , 2009 . - pp. 55-61

Kohnert, Axel:
Sets of type (d₁,d₂) in projective Hjelmslev planes over Galois rings.
In: Klin, Mikhail (Hrsg.): Algorithmic algebraic combinatorics and Gröbner bases. - Berlin; Heidelberg : Springer, 2009 . - pp. 269-278
DOI: https://doi.org/10.1007/978-3-642-01960-9_9

Bruin, Nils ; Stoll, Michael:
Two-cover descent on hyperelliptic curves.
In: Mathematics of Computation. Vol. 78 (2009) Issue 268 . - pp. 2347-2370.
DOI: https://doi.org/10.1090/S0025-5718-09-02255-8

2008

Volltext
Kohnert, Axel ; Kurz, Sascha:
Construction of large constant dimension codes with a prescribed minimum distance.
In: Jacques Calmet, Willi Geiselmann and Jörn Müller-Quade (Hrsg.): Mathematical methods in computer science: essays in memory of Thomas Beth. - Berlin : Springer, 2008 . - pp. 31-42 . - (Lecture Notes in Computer Science ; 5393 )

Volltext
Kohnert, Axel:
Construction of linear codes having prescribed primal-dual minimum distance with applications in cryptography.
In: Albanian Journal of Mathematics. Vol. 2 (2008) Issue 3 . - pp. 221-227.

Volltext
Bruin, Nils ; Stoll, Michael:
Deciding existence of rational points on curves : an experiment.
In: Experimental Mathematics. Vol. 17 (2008) Issue 2 . - pp. 181-189.

Cremona, John E. ; Fisher, Tom A. ; O'Neil, C. ; Simon, D. ; Stoll, Michael:
Explicit n-descent on elliptic curves, I. Algebra.
In: Journal für die Reine und Angewandte Mathematik. (2008) Issue 615 . - pp. 121-155.
DOI: https://doi.org/10.1515/CRELLE.2008.012

Volltext
Zwanzger, Johannes:
A heuristic algorithm for the construction of good linear codes.
In: IEEE Transactions on Information Theory. Vol. 54 (2008) Issue 5 . - pp. 2388-2392.
DOI: https://doi.org/10.1109/TIT.2008.920323

Stoll, Michael:
How to obtain global information from computations over finite fields.
In: Dmitry Kaledin, Yuri Tschinkel (editors): Higher-dimensional geometry over finite fields. - Amsterdam : IOS Press, 2008 . - pp. 189-196 . - (NATO Science for Peace and Security : Series D, Information and Communication Security ; 16 )

Bugeaud, Yann ; Mignotte, Maurice ; Siksek, Samir ; Stoll, Michael ; Tengely, Szabolcs:
Integral points on hyperelliptic curves.
In: Algebra & Number Theory. Vol. 2 (2008) Issue 8 . - pp. 859-885.
DOI: https://doi.org/10.2140/ant.2008.2.859

Kiermaier, Michael ; Wassermann, Alfred:
On the minimum Lee distance of quadratic residue codes over ℤ₄.
In: 2008 IEEE International Symposium on Information Theory proceedings. - Piscataway, NJ : Institute of Electrical and Electronics Engineers (IEEE), 2008 . - pp. 2617-2619
DOI: https://doi.org/10.1109/ISIT.2008.4595465

Stoll, Michael:
Rational 6-cycles under iteration of quadratic polynomials.
In: LMS Journal of Computation and Mathematics. Vol. 11 (2008) . - pp. 367-380.
DOI: https://doi.org/10.1112/S1461157000000644

2007

Stoll, Michael:
Applications of the Mordell-Weil sieve.
In: Oberwolfach Reports. Vol. 4 (2007) Issue 3 . - pp. 1967-1970.
DOI: https://doi.org/10.4171/OWR/2007/34

Kohnert, Axel:
Constructing two-weight codes with prescribed groups of automorphisms.
In: Discrete Applied Mathematics. Vol. 155 (2007) Issue 11 . - pp. 1451-1457.
DOI: https://doi.org/10.1016/j.dam.2007.03.006

Stoll, Michael:
Finite descent obstructions and rational points on curves.
In: Algebra & Number Theory. Vol. 1 (2007) Issue 4 . - pp. 349-391.
DOI: https://doi.org/10.2140/ant.2007.1.349

Volltext
Kohnert, Axel ; Kurz, Sascha:
A note on Erdős-Diophantine graphs and Diophantine carpets.
In: Mathematica Balkanica. New Series. Vol. 21 (2007) Issue 1–2 . - pp. 1-5.

Volltext
Poonen, Bjorn ; Schaefer, Edward F. ; Stoll, Michael:
Twists of X(7) and primitive solutions to x²+y³=z⁷.
In: Duke Mathematical Journal. Vol. 137 (2007) Issue 1 . - pp. 103-158.
DOI: https://doi.org/10.1215/S0012-7094-07-13714-1

2006

Kohnert, Axel:
Update on the extension of good linear codes.
In: Electronic Notes in Discrete Mathematics. Vol. 26 (1 September 2006) . - pp. 81-85.
DOI: https://doi.org/10.1016/j.endm.2006.08.015

Kurz, Sascha ; Kohnert, Axel:
Integral point sets over Z_n^m.
2006
Event: Optimal Discrete Structures and Algorithms (ODSA) 2006 , 04.-06.09.2006 , Rostock, Deutschland.
(Conference item: Workshop , Speech )

Wang, Min:
Canonical forms of discrete objects for databases and internet data exchange.
Bayreuth : Math. Inst. der Univ. Bayreuth , 2006 . - IX, 118 p. - (Bayreuther Mathematische Schriften ; 75 )
( Doctoral thesis, 2005 , Universität Bayreuth, Fakultät für Mathematik und Physik)

Betten, Anton ; Braun, Michael ; Fripertinger, Harald ; Kerber, Adalbert ; Kohnert, Axel ; Wassermann, Alfred:
Error-correcting linear codes : classification by isometry and applications.
Berlin : Springer , 2006 . - XXIX, 798 p. - (Algorithms and Computation in Mathematics ; 18 )
DOI: https://doi.org/10.1007/3-540-31703-1

Stoll, Michael:
Independence of rational points on twists of a given curve.
In: Compositio Mathematica. Vol. 142 (2006) Issue 5 . - pp. 1201-1214.
DOI: https://doi.org/10.1112/S0010437X06002168

Volltext
Schleicher, Dierk ; Stoll, Michael:
An introduction to Conway’s games and numbers.
In: Moscow Mathematical Journal. Vol. 6 (2006) Issue 2 . - pp. 359-388.

Volltext
Stoll, Michael:
On the number of rational squares at fixed distance from a fifth power.
In: Acta Arithmetica. Vol. 125 (2006) Issue 1 . - pp. 79-88.
DOI: https://doi.org/10.4064/aa125-1-7

2005

Volltext
Braun, Michael ; Kohnert, Axel ; Wassermann, Alfred:
Construction of (n,r)-arcs in PG(2,q).
In: Innovations in Incidence Geometry. Vol. 1 (2005) . - pp. 133-141.

Braun, Michael ; Kohnert, Axel ; Wassermann, Alfred:
Construction of (sometimes) optimal linear codes.
In: Kerber, Adalbert (ed.): ALCOMA '05. - Bayreuth : Mathemat. Inst. der Univ. Bayreuth, 2005 . - pp. 69-75 . - (Bayreuther Mathematische Schriften ; 74 )

Volltext
Stoll, Michael:
Finite coverings and rational points.
In: Oberwolfach Reports. Vol. 2 (2005) Issue 3 . - pp. 1824-1827.
DOI: https://doi.org/10.4171/OWR/2005/32

Braun, Michael ; Kohnert, Axel ; Wassermann, Alfred:
Optimal linear codes from matrix groups.
In: IEEE Transactions on Information Theory. Vol. 51 (2005) Issue 12 . - pp. 4247-4251.
DOI: https://doi.org/10.1109/TIT.2005.859291
Review:
  • AMS MatSciNet

2004

Kerber, Adalbert ; Kohnert, Axel:
Modular irreducible representations of the symmetric group as linear codes.
In: European Journal of Combinatorics. Vol. 25 (November 2004) Issue 8 . - pp. 1285-1299.
DOI: https://doi.org/10.1016/j.ejc.2003.10.009

Volltext
Kohnert, Axel:
Dominance order and graphical partitions.
In: The Electronic Journal of Combinatorics. Vol. 11 (2004) Issue 1 . - N4.

Schaefer, Edward F. ; Stoll, Michael:
How to do a p-descent on an elliptic curve.
In: Transactions of the American Mathematical Society. Vol. 356 (2004) Issue 3 . - pp. 1209-1231.
DOI: https://doi.org/10.1090/S0002-9947-03-03366-X

Haberberger, Evi:
Isomorphieklassifikation von Inzidenzstrukturen mit dem Lattice-Climbing-Verfahren am Beispiel von t-Designs.
Bayreuth : Math. Inst. der Univ. Bayreuth , 2004 . - VIII, 78 S. p. - (Bayreuther Mathematische Schriften ; 68 )
( Doctoral thesis, 2003 , Universität Bayreuth, Fakultät für Mathematik und Physik)

Braun, Michael:
Konstruktion diskreter Strukturen unter Verwendung von Operationen linearer Gruppen auf dem linearen Verband.
Bayreuth : Math. Inst. der Univ. Bayreuth , 2004 . - (Bayreuther Mathematische Schriften ; 69 )
( Doctoral thesis, 2003 , Universität Bayreuth, Fakultät für Mathematik und Physik)

Meringer, Markus:
Mathematische Modelle für die kombinatorische Chemie und die molekulare Strukturaufklärung.
Berlin : Logos-Verl. , 2004 . - XXXIV, 354 p.
( Doctoral thesis, 2004 , Universität Bayreuth, Fakultät für Mathematik und Physik)

2003

Geigant, Edith ; Stoll, Michael:
Bifurcation analysis of an orientational aggregation model.
In: Journal of Mathematical Biology. Vol. 46 (2003) Issue 6 . - pp. 537-563.
DOI: https://doi.org/10.1007/s00285-002-0187-1

Stoll, Michael ; Yang, Tonghai:
On the L-function of the curves y² = x⁵ + A.
In: Journal of the London Mathematical Society. Vol. 68 (2003) Issue 2 . - pp. 273-287.
DOI: https://doi.org/10.1112/S0024610703004460

Stoll, Michael ; Cremona, John E.:
On the reduction theory of binary forms.
In: Journal für die Reine und Angewandte Mathematik. (2003) Issue 565 . - pp. 79-99.
DOI: https://doi.org/10.1515/crll.2003.106

2002

Cremona, John E. ; Stoll, Michael:
Minimal models for 2-coverings of elliptic curves.
In: LMS Journal of Computation and Mathematics. Vol. 5 (2002) . - pp. 220-243.
DOI: https://doi.org/10.1112/S1461157000000760

Volltext
Stoll, Michael:
On the arithmetic of the curves y² = xˡ + A, II.
In: Journal of Number Theory. Vol. 93 (2002) Issue 2 . - pp. 183-206.
DOI: https://doi.org/10.1006/jnth.2001.2727

Stoll, Michael:
On the height constant for curves of genus two, II.
In: Acta Arithmetica. Vol. 104 (2002) Issue 2 . - pp. 165-182.
DOI: https://doi.org/10.4064/aa104-2-6

2001

Flynn, E. Victor ; Leprévost, Franck ; Schaefer, Edward F. ; Stein, William A. ; Stoll, Michael ; Wetherell, Joseph L.:
Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves.
In: Mathematics of Computation. Vol. 70 (2001) Issue 236 . - pp. 1675-1697.
DOI: https://doi.org/10.1090/S0025-5718-01-01320-5

Stoll, Michael:
Implementing 2-descent for Jacobians of hyperelliptic curves.
In: Acta Arithmetica. Vol. 98 (2001) Issue 3 . - pp. 245-277.
DOI: https://doi.org/10.4064/aa98-3-4

2000

Betten, Anton:
Schnittzahlen von Designs.
Bayreuth : Math. Inst. der Univ. Bayreuth , 2000 . - X, 131 p. - (Bayreuther Mathematische Schriften ; 58 )
( Doctoral thesis, 2000 , Universität Bayreuth, Fakultät für Mathematik und Physik)

1999

Volltext
Poonen, Bjorn ; Stoll, Michael:
The Cassels-Tate pairing on polarized abelian varieties.
In: Annals of Mathematics. Vol. 150 (1999) Issue 3 . - pp. 1109-1149.
DOI: https://doi.org/10.2307/121064

Volltext
Poonen, Bjorn ; Stoll, Michael:
A local-global principle for densities.
In: Ahlgren, Scott D. ; Andrews, George E. ; Ono, Ken (Hrsg.): Topics in Number Theory : in Honor of B. Gordon and S. Chowla. - Boston, MA : Springer US, 1999 . - pp. 241-244 . - (Mathematics and its Applications ; 467 )
DOI: https://doi.org/10.1007/978-1-4613-0305-3_16

Volltext
Stoll, Michael:
On the height constant for curves of genus two.
In: Acta Arithmetica. Vol. 90 (1999) Issue 2 . - pp. 183-201.

1998

Stoll, Michael:
On the arithmetic of the curves y² = xˡ + A and their Jacobians.
In: Journal für die Reine und Angewandte Mathematik. (1998) Issue 501 . - pp. 171-189.
DOI: https://doi.org/10.1515/crll.1998.076

Stoll, Michael:
On the asymptotics of the growth of 2-step nilpotent groups.
In: Journal of the London Mathematical Society. Vol. 58 (1998) Issue 1 . - pp. 38-48.
DOI: https://doi.org/10.1112/S0024610798006371

Schuster, S. ; Stoll, Michael:
A simple method to analyze resonators in fish hearing.
In: Elsner Norbert ; Wehner, Rüdiger (eds.): Proceedings of the 26th Göttingen Neurobiology Conference. Vol. 2. Göttingen neurobiology report 1998. - Stuttgart : Thieme, 1998 . - p. 303

Grüner, Thomas:
Strategien zur Konstruktion diskreter Strukturen.
1998 . - VI, 118 S.
( Doctoral thesis, 1998 , Universität Bayreuth, Fakultät für Mathematik, Physik und Informatik)

1997

Stoll, Michael:
Bounds for the length of recurrence relations for convolutions of P-recursive sequences.
In: European Journal of Combinatorics. Vol. 18 (August 1997) Issue 6 . - pp. 707-712.
DOI: https://doi.org/10.1006/eujc.1996.0123

Kohnert, Axel:
Multiplication of a Schubert polynomial by a Schur polynomial.
In: Annals of Combinatorics. Vol. 1 (1997) . - pp. 367-375.
DOI: https://doi.org/10.1007/BF02558487

Kohnert, Axel ; Veigneau, Sébastien:
Using Schubert basis to compute with multivariate polynomials.
In: Advances in Applied Mathematics. Vol. 19 (1997) Issue 1 . - pp. 45-60.
DOI: https://doi.org/10.1006/aama.1997.0526

1996

Stoll, Michael:
An example of a simple 2-dimensional abelian variety defined over Q with Mordell-Weil group of rank at least 20.
In: Comptes Rendus de l'Académie des Sciences. Series I. Vol. 322 (1996) Issue 9 . - pp. 849-851.

Stoll, Michael:
Rational and transcendental growth series for the higher Heisenberg groups.
In: Inventiones Mathematicae. Vol. 126 (1996) Issue 1 . - pp. 85-109.
DOI: https://doi.org/10.1007/s002220050090

1995

Stoll, Michael:
Regular geodesic languages for 2-step nilpotent groups.
In: Duncan, Andrew J. ; Gilbert, N. D. ; Howie, James (ed.): Combinatorial and geometric group theory : Edinburgh 1993. - Cambridge : Cambridge Univ. Press, 1995 . - pp. 294-299 . - (London Mathematical Society Lecture Note Series ; 204 )

Stoll, Michael:
Construction of semiabelian Galois extensions.
In: Glasgow Mathematical Journal. Vol. 37 (1995) Issue 1 . - pp. 99-104.
DOI: https://doi.org/10.1017/S0017089500030433

Grund, Roland:
Konstruktion molekularer Graphen mit gegebenen Hybridisierungen und überlappungsfreien Fragmenten.
Bayreuth : Lehrstuhl II für Mathematik , 1995 . - 223 p. - (Bayreuther Mathematische Schriften ; 49 )
( Doctoral thesis, 1994 , Universität Bayreuth, Fakultät für Mathematik, Physik und Informatik)

Barop, Christine:
Multiplizitätenfreie Untergruppenketten als Hilfsmittel in der Darstellungstheorie : Anwendungen auf die projektiven Darstellungen der symmetrischen Gruppe.
1995 . - VII, 129 S.
( Doctoral thesis, 1995 , Universität Bayreuth, Fakultät für Mathematik und Physik)

Stoll, Michael:
Two simple 2-dimensional abelian varieties defined over Q with Mordell-Weil group of rank at least 19.
In: Comptes Rendus de l'Académie des Sciences. Series I. Vol. 321 (1995) Issue 10 . - pp. 1341-1345.

1994

Volltext
Stoll, Michael:
Asymptotics of some number theoretic functions and an application to the growth of nilpotent groups.
Bonn , 1994 . - 67 p. - (Bonner mathematische Schriften ; 266 )
( Doctoral thesis, 1993 , Rheinische Friedrich-Wilhelms-Universität zu Bonn)

1992

Kohnert, Axel:
Schubert polynomials and skew Schur functions.
In: Journal of Symbolic Computation. Vol. 14 (1992) Issue 2–3 . - pp. 205-210.
DOI: https://doi.org/10.1016/0747-7171(92)90036-4

Kerber, Adalbert ; Kohnert, Axel ; Lascoux, Alain:
SYMMETRICA, an object oriented computer-algebra system for the symmetric group.
In: Journal of Symbolic Computation. Vol. 14 (1992) Issue 2–3 . - pp. 195-203.
DOI: https://doi.org/10.1016/0747-7171(92)90035-3

Schmalz, Bernd:
t-Designs zu vorgegebener Automorphismengruppe.
Bayreuth : Lehrstuhl II für Mathematik , 1992 . - 164 p. - (Bayreuther Mathematische Schriften ; 41 )
( Doctoral thesis, 1992 , Universität Bayreuth, Fakultät für Mathematik und Physik)

Stoll, Michael:
Galois groups overcℚ of some iterated polynomials.
In: Archiv der Mathematik. Vol. 59 (1992) . - pp. 239-244.
DOI: https://doi.org/10.1007/BF01197321

1991

Volltext
Kohnert, Axel:
Weintrauben, Polynome, Tableaux.
Bayreuth , 1991 . - 207 p. - (Bayreuther Mathematische Schriften ; 38 )
( Doctoral thesis, 1990 , Universität Bayreuth, Fakultät für Mathematik, Physik und Informatik)

1985

Stöcklein, Waldemar:
Spinresonanz an Radikalkationen-Salzen des Fluoranthens.
1985 . - 141 p.
( Doctoral thesis, 1985 , Universität Bayreuth, Fakultät für Mathematik und Physik)

1983

Golembiowski, Andreas:
Zur Darstellungstheorie der abzählbar unendlichen symmetrischen Gruppe über Körpern der Charakteristik 0.
Bayreuth , 1983 . - (Bayreuther Mathematische Schriften )
( Doctoral thesis, 1983 , Universität Bayreuth, Fakultät für Mathematik und Physik)

1981

Thürlings, Karl-Josef:
Eine Verallgemeinerung des Lemmas von Cauchy-Frobenius, kombinatorische und algebraische Zusammenhänge.
Bayreuth , 1981 . - S. 39 - 131 - (Bayreuther Mathematische Schriften ; 8 )
( Doctoral thesis, 1981 , Universität Bayreuth, Fakultät für Mathematik und Physik)

1980

Clausen, Michael:
Letter-Place-Algebren und ein charakteristik-freier Zugang zur Darstellungstheorie symmetrischer und voller linearer Gruppen.
Bayreuth , 1980 . - XVIII, 133 p. - (Bayreuther Mathematische Schriften ; 4 )
( Doctoral thesis, 1979 , Universität Bayreuth, Fakultät für Mathematik und Physik)

1979

Wagner, Bernd:
Charaktere symmetrischer und monomialer Gruppen als Polynomfunktionen.
Bayreuth , 1979 . - XII, 111, VII p. - (Bayreuther Mathematische Schriften ; 2 )
( Doctoral thesis, 1979 , Universität Bayreuth, Fakultät für Mathematik und Physik)

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