{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:TVZSQ4DUBBAH32I32XAWWJAZ4D","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":"007e333569a26150a6043d59c208868d251e9aa3245001c97c3a1580e8f61b43","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-03-09T14:43:32Z","title_canon_sha256":"d8c4869ed15ab5e709ba6f4bd2cb8388084b2a3faf1844817d98d7a4fc68eaab"},"schema_version":"1.0","source":{"id":"1903.04911","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.04911","created_at":"2026-05-17T23:51:28Z"},{"alias_kind":"arxiv_version","alias_value":"1903.04911v1","created_at":"2026-05-17T23:51:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.04911","created_at":"2026-05-17T23:51:28Z"},{"alias_kind":"pith_short_12","alias_value":"TVZSQ4DUBBAH","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"TVZSQ4DUBBAH32I3","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"TVZSQ4DU","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:227ad1d21184b6b3368dceb069c607e4e39017b238a060cb4342d55ccccfa8f4","target":"graph","created_at":"2026-05-17T23:51:28Z","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":"This paper considers the construction of isodual quasi-cyclic codes. First we prove that two quasi-cyclic codes are permutation equivalent if and only if their constituent codes are equivalent. This gives conditions on the existence of isodual quasi-cyclic codes. Then these conditions are used to obtain isodual quasi-cyclic codes. We also provide a construction for isodual quasi-cyclic codes as the matrix product of isodual codes.","authors_text":"Aicha Batoul, Fatma-Zahra Benahmed, Kenza Guenda, T. Aaron Gulliver","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-03-09T14:43:32Z","title":"Construction of Isodual Quasi-cyclic Codes over Finite Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.04911","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":"sha256:53d1605b4bf828761232d710c3abca5c457d1f93b0a412323a1cf9900f3e960f","target":"record","created_at":"2026-05-17T23:51:28Z","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":"007e333569a26150a6043d59c208868d251e9aa3245001c97c3a1580e8f61b43","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-03-09T14:43:32Z","title_canon_sha256":"d8c4869ed15ab5e709ba6f4bd2cb8388084b2a3faf1844817d98d7a4fc68eaab"},"schema_version":"1.0","source":{"id":"1903.04911","kind":"arxiv","version":1}},"canonical_sha256":"9d7328707408407de91bd5c16b2419e0ecdf3bb1337fcf5cfee49d23aae62bb9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d7328707408407de91bd5c16b2419e0ecdf3bb1337fcf5cfee49d23aae62bb9","first_computed_at":"2026-05-17T23:51:28.454226Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:28.454226Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qjoipSAK1n3OOnXyaBu7RX5uHZmo9ZLLCuBCNmnbYfdgCahYglIflLD5sQkPgbcyniwDoCoyGZ2zkRkmZqwJCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:28.454632Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.04911","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:53d1605b4bf828761232d710c3abca5c457d1f93b0a412323a1cf9900f3e960f","sha256:227ad1d21184b6b3368dceb069c607e4e39017b238a060cb4342d55ccccfa8f4"],"state_sha256":"b069f2a8083ed1bf59e08f65f1a38ab838e5c52cd70c0396a9208aaa609aff0e"}