{"paper":{"title":"On the Automorphism Group of a Binary Self-dual [120, 60, 24] Code","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.GR"],"primary_cat":"math.CO","authors_text":"Javier de la Cruz, Stefka Bouyuklieva, Wolfgang Willems","submitted_at":"2012-10-09T09:44:56Z","abstract_excerpt":"We prove that an automorphism of order 3 of a putative binary self-dual [120, 60, 24] code C has no fixed points. Moreover, the order of the automorphism group of C divides 2^a.3.5.7.19.23.29 where a is a nonegative integer. Automorphisms of odd composite order r may occur only for r=15, 57 or r=115 with corresponding cycle structures 15-(0,0,8;0), 57-(2,0,2;0) or 115-(1,0,1;0), respectively. In case that all involutions act fixed point freely we have |Aut(C)|<=920, and Aut(C) is solvable if it contains an element of prime order p>=7. Moreover, the alternating group A_5 is the only non-abelian"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2540","kind":"arxiv","version":1},"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"}