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Projective divisible binary codes

Title data

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 . - 10 S.

Official URL: Volltext

Project information

Project title:
Project's official titleProject's id
Integer Linear Programming Models for Subspace Codes and Finite GeometryNo information

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

For which positive integers n, k, and r does there exist a linear [n,k] code C over GF(q) with all codeword weights divisible by q^r and such that the columns of a generating matrix of C are projectively distinct? The motivation for studying this problem comes from the theory of partial spreads, or subspace codes with the highest possible minimum distance, since the set of holes of a partial spread of r-flats in PG(v-1,GF(q)) corresponds to a q^r-divisible code with k <= v. In this paper we provide an introduction to this problem and report on new results for the binary case q=2.

Abstract in another language

Für welche positiven ganzen Zahlen n, k und r gibst es einen linearen [n,k] Code C über GF(q) bei dem die Gewichte aller Codewörter durch q^r teilbar sind und die Spalten der Generatormatrix von C projektiv verschieden sind? Die Motivation für diese Fragestellung kommt aus der Theorie der partial spreads bzw. Teilraumcodes mit der größtmöglichen Minimaldistanz. Der Zusammenhang ist gegeben durch die Tatsache, dass die sogenannten Löcher eines partial r-spreads in PG(v-1,GF(q)) einem q^r-teilbaren Code mit k <= v entsprechen. Hier betrachten wir den binären Fall q=2 und geben eine Einführung in die Fragestellung der Existenz q^r-teilbarer linearer Codes.

Further data

Item Type: Article in a book
Refereed: Yes
Keywords: divisible codes; projective codes; partial spreads
Subject classification: Mathematics Subject Classification Code: 94B05 (51E23)
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II (Computer Algebra)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics and Didactics
Research Institutions > Research Centres > Forschungszentrum für Wissenschaftliches Rechnen an der Universität Bayreuth - HPC-Forschungszentrum
Research Institutions
Research Institutions > Research Centres
Result of work at the UBT: Yes
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
500 Science > 510 Mathematics
Date Deposited: 08 Dec 2017 07:41
Last Modified: 04 Dec 2019 10:42
URI: https://eref.uni-bayreuth.de/id/eprint/40887