{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:NTHQKBYP3MYULKFTQRHBAUUMWP","short_pith_number":"pith:NTHQKBYP","schema_version":"1.0","canonical_sha256":"6ccf05070fdb3145a8b3844e10528cb3e343b40b41e92ba7a0435af2d671c4f0","source":{"kind":"arxiv","id":"2407.15104","version":3},"attestation_state":"computed","paper":{"title":"The Support Designs of Several Families of Lifted Linear Codes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Cunsheng Ding, Qianqian Yan, Zhonghua Sun","submitted_at":"2024-07-21T10:04:50Z","abstract_excerpt":"A generator matrix of a linear code $\\C$ over $\\gf(q)$ is also a matrix of the same rank $k$ over any extension field $\\gf(q^\\ell)$ and generates a linear code of the same length, same dimension and same minimum distance over $\\gf(q^\\ell)$, denoted by $\\C(q|q^\\ell)$ and called a lifted code of $\\C$. Although $\\C$ and their lifted codes $\\C(q|q^\\ell)$ have the same parameters, they have different weight distributions and different applications. Few results about lifted linear codes are known in the literature. This paper proves some fundamental theory for lifted linear codes, and studies the su"},"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":"2407.15104","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2024-07-21T10:04:50Z","cross_cats_sorted":["math.CO","math.IT"],"title_canon_sha256":"da0e9eea039107f1c6ac14fa34f026d3012d96e51d321ebe80101e9cf40925a1","abstract_canon_sha256":"c23d38ff0230bd888a05afd6bd29686ede1da078ac6ca6491e1baf7a74a204a9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:52:55.631595Z","signature_b64":"ee+gb8mtlRgh7u54G37Y34zu2B+q2lmsiUJE8n3TJy+Z9ZLb9GgCTLtNU6PoydFINOpcM7+oTFTlN7p+6wymCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ccf05070fdb3145a8b3844e10528cb3e343b40b41e92ba7a0435af2d671c4f0","last_reissued_at":"2026-07-05T08:52:55.631081Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:52:55.631081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Support Designs of Several Families of Lifted Linear Codes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Cunsheng Ding, Qianqian Yan, Zhonghua Sun","submitted_at":"2024-07-21T10:04:50Z","abstract_excerpt":"A generator matrix of a linear code $\\C$ over $\\gf(q)$ is also a matrix of the same rank $k$ over any extension field $\\gf(q^\\ell)$ and generates a linear code of the same length, same dimension and same minimum distance over $\\gf(q^\\ell)$, denoted by $\\C(q|q^\\ell)$ and called a lifted code of $\\C$. Although $\\C$ and their lifted codes $\\C(q|q^\\ell)$ have the same parameters, they have different weight distributions and different applications. Few results about lifted linear codes are known in the literature. This paper proves some fundamental theory for lifted linear codes, and studies the su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.15104","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.15104/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2407.15104","created_at":"2026-07-05T08:52:55.631142+00:00"},{"alias_kind":"arxiv_version","alias_value":"2407.15104v3","created_at":"2026-07-05T08:52:55.631142+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.15104","created_at":"2026-07-05T08:52:55.631142+00:00"},{"alias_kind":"pith_short_12","alias_value":"NTHQKBYP3MYU","created_at":"2026-07-05T08:52:55.631142+00:00"},{"alias_kind":"pith_short_16","alias_value":"NTHQKBYP3MYULKFT","created_at":"2026-07-05T08:52:55.631142+00:00"},{"alias_kind":"pith_short_8","alias_value":"NTHQKBYP","created_at":"2026-07-05T08:52:55.631142+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/NTHQKBYP3MYULKFTQRHBAUUMWP","json":"https://pith.science/pith/NTHQKBYP3MYULKFTQRHBAUUMWP.json","graph_json":"https://pith.science/api/pith-number/NTHQKBYP3MYULKFTQRHBAUUMWP/graph.json","events_json":"https://pith.science/api/pith-number/NTHQKBYP3MYULKFTQRHBAUUMWP/events.json","paper":"https://pith.science/paper/NTHQKBYP"},"agent_actions":{"view_html":"https://pith.science/pith/NTHQKBYP3MYULKFTQRHBAUUMWP","download_json":"https://pith.science/pith/NTHQKBYP3MYULKFTQRHBAUUMWP.json","view_paper":"https://pith.science/paper/NTHQKBYP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2407.15104&json=true","fetch_graph":"https://pith.science/api/pith-number/NTHQKBYP3MYULKFTQRHBAUUMWP/graph.json","fetch_events":"https://pith.science/api/pith-number/NTHQKBYP3MYULKFTQRHBAUUMWP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NTHQKBYP3MYULKFTQRHBAUUMWP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NTHQKBYP3MYULKFTQRHBAUUMWP/action/storage_attestation","attest_author":"https://pith.science/pith/NTHQKBYP3MYULKFTQRHBAUUMWP/action/author_attestation","sign_citation":"https://pith.science/pith/NTHQKBYP3MYULKFTQRHBAUUMWP/action/citation_signature","submit_replication":"https://pith.science/pith/NTHQKBYP3MYULKFTQRHBAUUMWP/action/replication_record"}},"created_at":"2026-07-05T08:52:55.631142+00:00","updated_at":"2026-07-05T08:52:55.631142+00:00"}