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Honold, Thomas ; Kiermaier, Michael:
On putative q-analogues of the Fano plane and related combinatorial structures.
In: Hagen, Thomas ; Rupp, Florian ; Scheurle, Jürgen
(Hrsg.):
Dynamical Systems, Number Theory and Applications : A Festschrift in Honor of Armin Leutbecher’s 80th Birthday. -
New Jersey
: World Scientific
,
2016
. - S. 141-175
ISBN 978-981-4699-86-0
DOI: https://doi.org/10.1142/9789814699877_0008
Abstract
A set ℱq of 3-dimensional subspaces of GF(q)^7, the 7-dimensional vector space over the finite field GF(q), is said to form a q-analogue of the Fano plane if every 2-dimensional subspace of is contained in precisely one member of ℱq. The existence problem for such q-analogues remains unsolved for every single value of q. Here we report on an attempt to construct such q-analogues using ideas from the theory of subspace codes, which were introduced a few years ago by Koetter and Kschischang in their seminal work on error-correction for network coding. Our attempt eventually fails, but it produces the largest subspace codes known so far with the same parameters as a putative q-analogue. In particular we find a ternary subspace code of new record size 6977, and we are able to construct a binary subspace code of the largest currently known size 329 in an entirely computer-free manner.
Weitere Angaben
| Publikationsform: | Aufsatz in einem Buch |
|---|---|
| Begutachteter Beitrag: | Ja |
| Institutionen der Universität: | Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik II (Computeralgebra) Fakultäten Fakultäten > Fakultät für Mathematik, Physik und Informatik Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut |
| Titel an der UBT entstanden: | Ja |
| Themengebiete aus DDC: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
| Eingestellt am: | 11 Apr 2016 07:07 |
| Letzte Änderung: | 11 Aug 2023 07:26 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/32156 |