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Combining this with the previously proved result by Bouyuklieva that such a code cannot have an automorphism group containing an involution with fixed points, we conclude that the automorphism group of the $[72,36,16]$-code cannot be of even order, leaving 3 and 5 as the only possibilities."},"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":"1303.4920","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-20T12:28:55Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"6c386daeca3a081bdc911b6350b1410e2c909023786727a325776848e6c3f73a","abstract_canon_sha256":"7d382226293097a82aca3d94db9b05465fdb42cbe97f73a417c4305d3c95acda"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:01.857663Z","signature_b64":"60txalr1XxSPPScymYKlxwB3XcWI/X1smt61cU9e5/6OKF7v2642Z1gse/ghmMjdoJucpIM156qnPP7u6kv3Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4238af460eb8523c3adeffc57f2bc95fcce565ca2f19441b2ff1654cea37baa5","last_reissued_at":"2026-05-18T03:30:01.857142Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:01.857142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The automorphism group of the doubly-even [72,36,16] code can only be of order 1, 3 or 5","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.CO","authors_text":"Bahattin Yildiz, Steven T Dougherty, Suat Karadeniz","submitted_at":"2013-03-20T12:28:55Z","abstract_excerpt":"We prove that a putative $[72,36,16]$ code is not the image of linear code over $\\ZZ_4$, $\\FF_2 + u \\FF_2$ or $\\FF_2+v\\FF_2$, thus proving that the extremal doubly even $[72,36,16]$-binary code cannot have an automorphism group containing a fixed point-free involution. Combining this with the previously proved result by Bouyuklieva that such a code cannot have an automorphism group containing an involution with fixed points, we conclude that the automorphism group of the $[72,36,16]$-code cannot be of even order, leaving 3 and 5 as the only possibilities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4920","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1303.4920","created_at":"2026-05-18T03:30:01.857225+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.4920v2","created_at":"2026-05-18T03:30:01.857225+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4920","created_at":"2026-05-18T03:30:01.857225+00:00"},{"alias_kind":"pith_short_12","alias_value":"II4K6RQOXBJD","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"II4K6RQOXBJDYOW6","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"II4K6RQO","created_at":"2026-05-18T12:27:46.883200+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/II4K6RQOXBJDYOW677CX6K6JL7","json":"https://pith.science/pith/II4K6RQOXBJDYOW677CX6K6JL7.json","graph_json":"https://pith.science/api/pith-number/II4K6RQOXBJDYOW677CX6K6JL7/graph.json","events_json":"https://pith.science/api/pith-number/II4K6RQOXBJDYOW677CX6K6JL7/events.json","paper":"https://pith.science/paper/II4K6RQO"},"agent_actions":{"view_html":"https://pith.science/pith/II4K6RQOXBJDYOW677CX6K6JL7","download_json":"https://pith.science/pith/II4K6RQOXBJDYOW677CX6K6JL7.json","view_paper":"https://pith.science/paper/II4K6RQO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.4920&json=true","fetch_graph":"https://pith.science/api/pith-number/II4K6RQOXBJDYOW677CX6K6JL7/graph.json","fetch_events":"https://pith.science/api/pith-number/II4K6RQOXBJDYOW677CX6K6JL7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/II4K6RQOXBJDYOW677CX6K6JL7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/II4K6RQOXBJDYOW677CX6K6JL7/action/storage_attestation","attest_author":"https://pith.science/pith/II4K6RQOXBJDYOW677CX6K6JL7/action/author_attestation","sign_citation":"https://pith.science/pith/II4K6RQOXBJDYOW677CX6K6JL7/action/citation_signature","submit_replication":"https://pith.science/pith/II4K6RQOXBJDYOW677CX6K6JL7/action/replication_record"}},"created_at":"2026-05-18T03:30:01.857225+00:00","updated_at":"2026-05-18T03:30:01.857225+00:00"}