Automorphisms of doubly-even self-dual binary codes

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.

Added a new proof for the main result

Cited by in corpus (3)

• Self-dual Permutation Codes of Finite Groups in Semisimple Case
• An extremal [72,36,16] binary code has no automorphism group containing Z2xZ4, Q_8, or Z_{10}
• On involutions in extremal self-dual codes and the dual distance of semi self-dual codes