Automorphisms of Extremal Self-Dual Codes
Stefka Bouyuklieva, Anton Malevich, Wolfgang M. Willems · IEEE Transactions on Information Theory · 2010
LetCbe a binary extremal self-dual code of lengthn¿ 48. We prove that for each¿ ¿ Aut(C) of prime orderp¿ 5 the number of fixed points in the permutation action on the coordinate positions is bounded by the number ofp-cycles. It turns out that large primesp, i.e.,n-psmall, seem to occur in|Aut(C)| very rarely. Examples are the extended quadratic residue codes. We further prove that doubly even extended quadratic residue codes of lengthn=p+ 1 are extremal only in the casesn=8, 24, 32, 48, 80, and 104.