A subspace code of size 333 in the setting of a binary q-analog of the Fano plane

Titelangaben

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. Bd. 13 (2019) Heft 3 . - S. 457-475.
ISSN 1930-5346
DOI: https://doi.org/10.3934/amc.2019029

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Abstract

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.