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

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, i.e., $333\le A_2(7,4;3)$, 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 one of $31$ 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.

18 pages; typos corrected

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Cited by in corpus (1)

• On $\alpha$-points of $q$-analogs of the Fano plane