## Title data

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

ISBN 978-981-4699-86-0

DOI: https://doi.org/10.1142/9789814699877_0008

## Abstract in another language

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.

## Further data

Item Type: | Article in a book |
---|---|

Refereed: | Yes |

Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II (Computer Algebra) Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics |

Result of work at the UBT: | Yes |

DDC Subjects: | 500 Science > 510 Mathematics |

Date Deposited: | 11 Apr 2016 07:07 |

Last Modified: | 11 Aug 2023 07:26 |

URI: | https://eref.uni-bayreuth.de/id/eprint/32156 |