Permutation groups and binary self-orthogonal codes

Abstract

Let G be a permutation group on an n-element set Ω. We study the binary code C ( G , Ω ) defined as the dual code of the code spanned by the sets of fixed points of involutions of G. We show that any G-invariant self-orthogonal code of length n is contained in C ( G , Ω ) . Many self-orthogonal codes related to sporadic simple groups, including the extended Golay code, are obtained as C ( G , Ω ) . Some new self-dual codes invariant under sporadic almost simple groups are constructed.