{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:TVZSQ4DUBBAH32I32XAWWJAZ4D","short_pith_number":"pith:TVZSQ4DU","canonical_record":{"source":{"id":"1903.04911","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-03-09T14:43:32Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"d8c4869ed15ab5e709ba6f4bd2cb8388084b2a3faf1844817d98d7a4fc68eaab","abstract_canon_sha256":"007e333569a26150a6043d59c208868d251e9aa3245001c97c3a1580e8f61b43"},"schema_version":"1.0"},"canonical_sha256":"9d7328707408407de91bd5c16b2419e0ecdf3bb1337fcf5cfee49d23aae62bb9","source":{"kind":"arxiv","id":"1903.04911","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:TVZSQ4DUBBAH32I32XAWWJAZ4D","target":"record","payload":{"canonical_record":{"source":{"id":"1903.04911","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-03-09T14:43:32Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"d8c4869ed15ab5e709ba6f4bd2cb8388084b2a3faf1844817d98d7a4fc68eaab","abstract_canon_sha256":"007e333569a26150a6043d59c208868d251e9aa3245001c97c3a1580e8f61b43"},"schema_version":"1.0"},"canonical_sha256":"9d7328707408407de91bd5c16b2419e0ecdf3bb1337fcf5cfee49d23aae62bb9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:28.454632Z","signature_b64":"qjoipSAK1n3OOnXyaBu7RX5uHZmo9ZLLCuBCNmnbYfdgCahYglIflLD5sQkPgbcyniwDoCoyGZ2zkRkmZqwJCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d7328707408407de91bd5c16b2419e0ecdf3bb1337fcf5cfee49d23aae62bb9","last_reissued_at":"2026-05-17T23:51:28.454226Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:28.454226Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.04911","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:51:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZtJ6MXLFR9lsqLHWFFkM7mhh8lY4DfoNJnMjBxcsWxoxSGLLv5Jrnj1qk4eocrFfgFpnQfoNFjR7aQxQJGo5BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:45:01.444531Z"},"content_sha256":"53d1605b4bf828761232d710c3abca5c457d1f93b0a412323a1cf9900f3e960f","schema_version":"1.0","event_id":"sha256:53d1605b4bf828761232d710c3abca5c457d1f93b0a412323a1cf9900f3e960f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:TVZSQ4DUBBAH32I32XAWWJAZ4D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Construction of Isodual Quasi-cyclic Codes over Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Aicha Batoul, Fatma-Zahra Benahmed, Kenza Guenda, T. Aaron Gulliver","submitted_at":"2019-03-09T14:43:32Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.04911","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:51:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zBgJok5/kMQyUrYoQO6koRvdsD2mZjOK0xy/gBWThgT7J7pWwNyf81+nnpWFKyN67kfZwnDy1w9pmGC44VMBCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:45:01.445219Z"},"content_sha256":"227ad1d21184b6b3368dceb069c607e4e39017b238a060cb4342d55ccccfa8f4","schema_version":"1.0","event_id":"sha256:227ad1d21184b6b3368dceb069c607e4e39017b238a060cb4342d55ccccfa8f4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TVZSQ4DUBBAH32I32XAWWJAZ4D/bundle.json","state_url":"https://pith.science/pith/TVZSQ4DUBBAH32I32XAWWJAZ4D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TVZSQ4DUBBAH32I32XAWWJAZ4D/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T14:45:01Z","links":{"resolver":"https://pith.science/pith/TVZSQ4DUBBAH32I32XAWWJAZ4D","bundle":"https://pith.science/pith/TVZSQ4DUBBAH32I32XAWWJAZ4D/bundle.json","state":"https://pith.science/pith/TVZSQ4DUBBAH32I32XAWWJAZ4D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TVZSQ4DUBBAH32I32XAWWJAZ4D/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mDhKcca+IXjLDKeauRRAnNiwtETPaxsOUvDgRkwAira5T0B1M3jP8FMmRArkXvZYg37hBLvSmE4VuOdrLQG/DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T14:45:01.449241Z","bundle_sha256":"1f1fe71390b3e5229a891e44b0c08f1d47f668c9c104812932559484560f971a"}}