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arXiv · 0810.3787

Automorphisms of doubly-even self-dual binary codes

Annika Guenther·Gabriele Nebe
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Abstract

The automorphism group of a binary doubly-even self-dual code is always contained in the alternating group. On the other hand, given a permutation group $G$ of degree $n$ there exists a doubly-even self-dual $G$-invariant code if and only if $n$ is a multiple of 8, every simple self-dual $\F_2G$-module occurs with even multiplicity in $\F_2^n$, and $G$ is contained in the alternating group.

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Annika Guenther, Gabriele Nebe. 2009-04-08. Automorphisms of doubly-even self-dual binary codes. https://doi.org/10.1112/blms%2Fbdp026

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