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

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.
Bayreuth
,
2017
. - 17 p.

Ganzzahlige Optimierungsmodelle für Subspace Codes und endliche Geometrie

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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.

Further data

Item Type:

Preprint, postprint, working paper, discussion paper