Improved bounds and classification results for binary subspace codes

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Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha:
Improved bounds and classification results for binary subspace codes.
2015
Veranstaltung: 7th Workshop on Coding and Systems , 01.-03.07.2015 , Salamanca, Spain.
(Veranstaltungsbeitrag: Workshop , Vortrag )

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Abstract

In contrast to constant dimension codes the dimensions of the codewords can be arbitrary for so-called subspace codes.
We consider binary subspace codes. Given the dimension $n$ of the ambient space $\mathbb{F}_2^n$ and the subspace distance $d$ the question for the maximal cardinality $A_2^S(n,d;[0,n])$ arises. We provide improved bounds and classification results for the extremal subspace codes. In particular we show $A_2^S(7,5;[0,7])=34$, which closes a gap, and classify all optimal codes up to isomorphism.