Automorphisms of doubly even self-dual binary codes
Annika Günther, Gabriele Nebe · Bulletin of the London Mathematical Society · 2009
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 multiple of 8, every simple self-dual F2G-module occurs with even multiplicity in Fn 2, and G is contained in the alternating group. 1 Introduction. Self-dual binary codes have become of great interest, also because of Gleason’s theorem [4] that establishes a connection between coding theory and invariant theory of finite groups. The best known self-dual codes have the additional property of being doubly-even, which means that the weight of every codeword is divisible by 4 (see Definition 2.1). It follows