{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:TFFDPEMDOKTJ5XA7V2SWFZYFZH","short_pith_number":"pith:TFFDPEMD","schema_version":"1.0","canonical_sha256":"994a37918372a69edc1faea562e705c9e6a2fb12f7a610a3199de9ce704d4a0f","source":{"kind":"arxiv","id":"1309.1621","version":1},"attestation_state":"computed","paper":{"title":"Skew Generalized 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":"Fang-Wei Fu, Jian Gao, Linzhi Shen","submitted_at":"2013-09-06T12:50:37Z","abstract_excerpt":"In this work, we study a class of generalized quasi-cyclic (GQC) codes called skew GQC codes. By the factorization theory of ideals, we give the Chinese Remainder Theorem over the skew polynomial ring, which leads to a canonical decomposition of skew GQC codes. We also focus on some characteristics of skew GQC codes in details. For a 1-generator skew GQC code, we define the parity-check polynomial, determine the dimension and give a lower bound on the minimum Hamming distance. The skew quasi-cyclic (QC) codes are also discussed briefly."},"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":"1309.1621","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-09-06T12:50:37Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"7b26b628a6ca67d7dd73dc559a6a48509ad28413cdc2fb778488a9e9d294a0cd","abstract_canon_sha256":"46ee59d22244b6b6bf7c544879d397ffb062a4b3a3f66fcc7e15385fa17bdddc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:59.020620Z","signature_b64":"uglyXlJyz5siF1GMsAneFQfAM+ZiU34tQuJjemoP/O4Ez2M8QH+YxtlNoVKasg5gDk/1EhkgZ68H9rNrsH9dBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"994a37918372a69edc1faea562e705c9e6a2fb12f7a610a3199de9ce704d4a0f","last_reissued_at":"2026-05-18T03:13:59.019860Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:59.019860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Skew Generalized 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":"Fang-Wei Fu, Jian Gao, Linzhi Shen","submitted_at":"2013-09-06T12:50:37Z","abstract_excerpt":"In this work, we study a class of generalized quasi-cyclic (GQC) codes called skew GQC codes. By the factorization theory of ideals, we give the Chinese Remainder Theorem over the skew polynomial ring, which leads to a canonical decomposition of skew GQC codes. We also focus on some characteristics of skew GQC codes in details. For a 1-generator skew GQC code, we define the parity-check polynomial, determine the dimension and give a lower bound on the minimum Hamming distance. The skew quasi-cyclic (QC) codes are also discussed briefly."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1621","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1309.1621","created_at":"2026-05-18T03:13:59.019981+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.1621v1","created_at":"2026-05-18T03:13:59.019981+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1621","created_at":"2026-05-18T03:13:59.019981+00:00"},{"alias_kind":"pith_short_12","alias_value":"TFFDPEMDOKTJ","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_16","alias_value":"TFFDPEMDOKTJ5XA7","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_8","alias_value":"TFFDPEMD","created_at":"2026-05-18T12:28:02.375192+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/TFFDPEMDOKTJ5XA7V2SWFZYFZH","json":"https://pith.science/pith/TFFDPEMDOKTJ5XA7V2SWFZYFZH.json","graph_json":"https://pith.science/api/pith-number/TFFDPEMDOKTJ5XA7V2SWFZYFZH/graph.json","events_json":"https://pith.science/api/pith-number/TFFDPEMDOKTJ5XA7V2SWFZYFZH/events.json","paper":"https://pith.science/paper/TFFDPEMD"},"agent_actions":{"view_html":"https://pith.science/pith/TFFDPEMDOKTJ5XA7V2SWFZYFZH","download_json":"https://pith.science/pith/TFFDPEMDOKTJ5XA7V2SWFZYFZH.json","view_paper":"https://pith.science/paper/TFFDPEMD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.1621&json=true","fetch_graph":"https://pith.science/api/pith-number/TFFDPEMDOKTJ5XA7V2SWFZYFZH/graph.json","fetch_events":"https://pith.science/api/pith-number/TFFDPEMDOKTJ5XA7V2SWFZYFZH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TFFDPEMDOKTJ5XA7V2SWFZYFZH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TFFDPEMDOKTJ5XA7V2SWFZYFZH/action/storage_attestation","attest_author":"https://pith.science/pith/TFFDPEMDOKTJ5XA7V2SWFZYFZH/action/author_attestation","sign_citation":"https://pith.science/pith/TFFDPEMDOKTJ5XA7V2SWFZYFZH/action/citation_signature","submit_replication":"https://pith.science/pith/TFFDPEMDOKTJ5XA7V2SWFZYFZH/action/replication_record"}},"created_at":"2026-05-18T03:13:59.019981+00:00","updated_at":"2026-05-18T03:13:59.019981+00:00"}