## Title data

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.

ISSN 1930-5346

DOI: https://doi.org/10.3934/amc.2019029

## Project information

Project title: |
Project's official title Project's id Ganzzahlige Optimierungsmodelle für Subspace Codes und endliche Geometrie No information |
---|---|

Project financing: |
Deutsche Forschungsgemeinschaft |

## Abstract in another language

We show that there is a binary subspace code of constant dimension 3 in ambient dimension 7, having minimum distance 4 and cardinality 333,, which improves the previous best known lower bound of 329. Moreover, if a code with these parameters has at least 333 elements, its automorphism group is in 31 conjugacy classes. This is achieved by a more general technique for an exhaustive search in a finite group that does not depend on the enumeration of all subgroups.