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 gp 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(gp) which consists of the set of fixed points of gp, we prove that C is a projective F2g module if and only if a natural projection of C(gp) is a self-dual code. We then discuss easy-to-handle criteria to decide if C 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. © 1963-2012 IEEE.


Published in:
IEEE Transactions on Information Theory
Year:
2013
Publisher:
Institute of Electrical and Electronics Engineers
ISSN:
0018-9448
Laboratories:




 Record created 2015-09-02, last modified 2018-01-28

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