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

The work was supported by the ICT COST Action IC1104 and grants KU 2430/3-1, WA 1666/9-1 – "Integer Linear Programming Models for Subspace Codes and Finite Geometry" – from the German Research Foundation

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  • We show that there is a binary subspace code of constant dimension 3 in ambient dimension 7, having minimum subspace 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.

    Mathematics Subject Classification: Primary: 51E20; Secondary: 05B07, 11T71, 94B25.


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