{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TTOUTHB7PYTGHUAW6O53UAEILS","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"36afc54267770e7cb9432516b6eb96c15dc379074e61e45130e69423e11e05e5","cross_cats_sorted":["math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-07-06T21:34:56Z","title_canon_sha256":"0898880044efa98c898da5eaabdd72bb9aae4a9f8bb69131e7c9a82921ca42a0"},"schema_version":"1.0","source":{"id":"1507.01628","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.01628","created_at":"2026-05-18T01:20:11Z"},{"alias_kind":"arxiv_version","alias_value":"1507.01628v1","created_at":"2026-05-18T01:20:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01628","created_at":"2026-05-18T01:20:11Z"},{"alias_kind":"pith_short_12","alias_value":"TTOUTHB7PYTG","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TTOUTHB7PYTGHUAW","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TTOUTHB7","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:e1cd34c7f8c3de0cdcf9f263409cf723bbd23b29a573270251a12be150fdfcb7","target":"graph","created_at":"2026-05-18T01:20:11Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this work, we propose a modified four circulant construction for self-dual codes and a bordered version of the construction using the properties of \\lambda-circulant and \\lambda-reverse circulant matrices. By using the constructions on $F_2$, we obtain new binary codes of lengths 64 and 68. We also apply the constructions to the ring $R_2$ and considering the $F_2$ and $R_1$-extensions, we obtain new singly-even extremal binary self-dual codes of lengths 66 and 68. More precisely, we find 3 new codes of length 64, 15 new codes of length 66 and 22 new codes of length 68. These codes all have","authors_text":"Abdullah Pa\\c{s}a, Abidin Kaya, Bahattin Yildiz","cross_cats":["math.CO","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-07-06T21:34:56Z","title":"New extremal binary self-dual codes from a modified four circulant construction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01628","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:fde3fea6b1a42dcc0b9e84b8704ec090cdcbda9abc869dbd1114367a9a984356","target":"record","created_at":"2026-05-18T01:20:11Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"36afc54267770e7cb9432516b6eb96c15dc379074e61e45130e69423e11e05e5","cross_cats_sorted":["math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-07-06T21:34:56Z","title_canon_sha256":"0898880044efa98c898da5eaabdd72bb9aae4a9f8bb69131e7c9a82921ca42a0"},"schema_version":"1.0","source":{"id":"1507.01628","kind":"arxiv","version":1}},"canonical_sha256":"9cdd499c3f7e2663d016f3bbba00885c945dbf3b9dee72a08e570d94d0a7620c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9cdd499c3f7e2663d016f3bbba00885c945dbf3b9dee72a08e570d94d0a7620c","first_computed_at":"2026-05-18T01:20:11.633841Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:11.633841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u+S3J020lqy9721Xln+0O4L/okloSIapS2Ssf3PQZ+KoXpZDYSxnOppZxcqnE7Y4O/sag/lnrgsF5XXtpieiCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:11.634600Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.01628","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fde3fea6b1a42dcc0b9e84b8704ec090cdcbda9abc869dbd1114367a9a984356","sha256:e1cd34c7f8c3de0cdcf9f263409cf723bbd23b29a573270251a12be150fdfcb7"],"state_sha256":"6c86b27bd2be784144f3b2f9680a0d351c82ba9fad9b9115a641ead264c9ab4c"}