{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:4RP4PG2WUDUI5S7TXYVD5FY2F5","short_pith_number":"pith:4RP4PG2W","schema_version":"1.0","canonical_sha256":"e45fc79b56a0e88ecbf3be2a3e971a2f5930a678782043868d5133f558102dfe","source":{"kind":"arxiv","id":"2506.23081","version":1},"attestation_state":"computed","paper":{"title":"Linear Complementary Pairs of Algebraic Geometry Codes via Kummer Extensions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Chen Haojie, Huang Junjie, Zhang Huachao, Zhao Chang-An","submitted_at":"2025-06-29T04:21:05Z","abstract_excerpt":"Due to their widespread applications, linear complementary pairs (LCPs) have attracted much attention in recent years. In this paper, we determine explicit construction of non-special divisors of degree $g$ and $g-1$ on Kummer extensions with specific properties. In addition, we present several methods for constructing LCPs of algebraic geometry codes (AG Codes) via Kummer extensions. These results are applied in constructing explicit LCPs of AG Codes from subcovers of the BM curve, elliptic function fields, hyperelliptic function fields and other function fields. It is important to mention th"},"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":"2506.23081","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2025-06-29T04:21:05Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"63aa19e60e3445ea80fe94f4f575b074bf41056872b051cdbd0bd8bb6033b5c4","abstract_canon_sha256":"f834b2032b6e91a68ed74c74a9b1ba5119e8e2714e5d657146baec23198d150b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:28:50.642849Z","signature_b64":"+UaDgid6GUx/KtxpmmhFIS97UEArjesvg82T2oBUZO2JzFqlE6FkNSAV837a0VpWxFXVgi1sqp817rHgpRsoCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e45fc79b56a0e88ecbf3be2a3e971a2f5930a678782043868d5133f558102dfe","last_reissued_at":"2026-07-05T11:28:50.642331Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:28:50.642331Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Linear Complementary Pairs of Algebraic Geometry Codes via Kummer Extensions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Chen Haojie, Huang Junjie, Zhang Huachao, Zhao Chang-An","submitted_at":"2025-06-29T04:21:05Z","abstract_excerpt":"Due to their widespread applications, linear complementary pairs (LCPs) have attracted much attention in recent years. In this paper, we determine explicit construction of non-special divisors of degree $g$ and $g-1$ on Kummer extensions with specific properties. In addition, we present several methods for constructing LCPs of algebraic geometry codes (AG Codes) via Kummer extensions. These results are applied in constructing explicit LCPs of AG Codes from subcovers of the BM curve, elliptic function fields, hyperelliptic function fields and other function fields. It is important to mention th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.23081","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.23081/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":"2506.23081","created_at":"2026-07-05T11:28:50.642408+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.23081v1","created_at":"2026-07-05T11:28:50.642408+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.23081","created_at":"2026-07-05T11:28:50.642408+00:00"},{"alias_kind":"pith_short_12","alias_value":"4RP4PG2WUDUI","created_at":"2026-07-05T11:28:50.642408+00:00"},{"alias_kind":"pith_short_16","alias_value":"4RP4PG2WUDUI5S7T","created_at":"2026-07-05T11:28:50.642408+00:00"},{"alias_kind":"pith_short_8","alias_value":"4RP4PG2W","created_at":"2026-07-05T11:28:50.642408+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.11764","citing_title":"Non-special Divisors, LCPs of Codes, and LCD Codes on Kummer Extensions","ref_index":26,"is_internal_anchor":false},{"citing_arxiv_id":"2605.14046","citing_title":"Construction of Non-special Divisors on Kummer Covers With Arbritary Ramification For LCP Codes","ref_index":7,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4RP4PG2WUDUI5S7TXYVD5FY2F5","json":"https://pith.science/pith/4RP4PG2WUDUI5S7TXYVD5FY2F5.json","graph_json":"https://pith.science/api/pith-number/4RP4PG2WUDUI5S7TXYVD5FY2F5/graph.json","events_json":"https://pith.science/api/pith-number/4RP4PG2WUDUI5S7TXYVD5FY2F5/events.json","paper":"https://pith.science/paper/4RP4PG2W"},"agent_actions":{"view_html":"https://pith.science/pith/4RP4PG2WUDUI5S7TXYVD5FY2F5","download_json":"https://pith.science/pith/4RP4PG2WUDUI5S7TXYVD5FY2F5.json","view_paper":"https://pith.science/paper/4RP4PG2W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.23081&json=true","fetch_graph":"https://pith.science/api/pith-number/4RP4PG2WUDUI5S7TXYVD5FY2F5/graph.json","fetch_events":"https://pith.science/api/pith-number/4RP4PG2WUDUI5S7TXYVD5FY2F5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4RP4PG2WUDUI5S7TXYVD5FY2F5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4RP4PG2WUDUI5S7TXYVD5FY2F5/action/storage_attestation","attest_author":"https://pith.science/pith/4RP4PG2WUDUI5S7TXYVD5FY2F5/action/author_attestation","sign_citation":"https://pith.science/pith/4RP4PG2WUDUI5S7TXYVD5FY2F5/action/citation_signature","submit_replication":"https://pith.science/pith/4RP4PG2WUDUI5S7TXYVD5FY2F5/action/replication_record"}},"created_at":"2026-07-05T11:28:50.642408+00:00","updated_at":"2026-07-05T11:28:50.642408+00:00"}