{"paper":{"title":"Automorphism of order 2p in binary self-dual extremal codes of length a multiple of 24","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.RT"],"primary_cat":"cs.IT","authors_text":"Martino Borello, Wolfgang Willems","submitted_at":"2012-09-23T15:06:00Z","abstract_excerpt":"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<g>-module if and only if a natural projection of C(g^p) is a self-dual code. We then discuss easy to hand"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5071","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}