Automorphisms of Order 2p in Binary Self-Dual Extremal Codes of Length a Multiple of 24
Let C be a binary self-dual code with an automorphism g of order 2p, where p is an odd prime, such that g(p) is a fixed point free involution. If C is extremal of length a multiple of 24, all the involutions are fixed point free, except the Golay Code and eventually putative codes of length 120. Connecting module theoretical properties of a self-dual code C with coding theoretical ones of the subcode C(g(p)) which consists of the set of fixed points of g(p), we prove that C is a projective F-2  -module if and only if a natural projection of C(g(p)) is a self-dual code. We then discuss easy-to-handle criteria to decide if is projective or not. As an application, we consider in the last part extremal self-dual codes of length 120, proving that their automorphism group does not contain elements of order 38 and 58.
self-dual codes automorphism group