Automorphisms of doubly-even self-dual binary codes

Details Automorphisms of doubly-even self-dual binary codes Automorphisms of doubly-even self-dual binary codes

2008-10-21

arxiv.org/abs/0810.3787v2

Mathematics

Number Theory

Added a new proof for the main result

Scientific paper

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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