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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1210.2540","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-09T09:44:56Z","cross_cats_sorted":["cs.DM","math.GR"],"title_canon_sha256":"31991d9768f73c3f755420c42db1acfd602fb36f697d1e100ebe3f36775f7ee5","abstract_canon_sha256":"572e75d600941ff031d02384f93440041852e3a7c7ea12b233766ec1a805de1a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:24.391950Z","signature_b64":"orUHnkf661blD96biWSdhX3cjuqXo7Npvm+REDy6wpRi0BiFQcO+ua5E3bl11OQSp+E5Lrlx2eq6rh3hvWaACw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"11ecb6d671c683d0b0d28cf04ed8594ed80d6c3263aac2908d958840494a33dd","last_reissued_at":"2026-05-18T00:05:24.391490Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:24.391490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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