{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:DPGAPSPMSUW57GNN4ZYINQYKHB","short_pith_number":"pith:DPGAPSPM","schema_version":"1.0","canonical_sha256":"1bcc07c9ec952ddf99ade67086c30a38539f0843bd513cf0189458bc301c0876","source":{"kind":"arxiv","id":"1501.07431","version":1},"attestation_state":"computed","paper":{"title":"Negacyclic codes of odd length over the ring $\\mathbb{F}_p[u,v]/\\langle u^2,v^2,uv-vu\\rangle$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Bappaditya Ghosh","submitted_at":"2015-01-29T12:17:17Z","abstract_excerpt":"We discuss the structure of negacyclic codes of odd length over the ring $\\mathbb{F}_p[u, v]/ \\langle u^2, v^2, uv-vu \\rangle$. We find the unique generating set, the rank and the minimum distance for these negacyclic codes."},"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":"1501.07431","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-29T12:17:17Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"345e23a1cc69e692225e88e05ca8ca761a6cbcd361e6339ca6a8ec3e37c34a57","abstract_canon_sha256":"2a2c3af54e3dab5716e33191186b1125005578f6fa23bcf3713cceda1d254d68"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:21.945152Z","signature_b64":"PGh63EWso8cr8jjhGb7sJ5jKcLrz4gS5Br8jNkJqAwwX4OQvszU8phBxtgcqC08dMb1EVqaIvH/OUUXIGcZBBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1bcc07c9ec952ddf99ade67086c30a38539f0843bd513cf0189458bc301c0876","last_reissued_at":"2026-05-18T02:28:21.944535Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:21.944535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Negacyclic codes of odd length over the ring $\\mathbb{F}_p[u,v]/\\langle u^2,v^2,uv-vu\\rangle$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Bappaditya Ghosh","submitted_at":"2015-01-29T12:17:17Z","abstract_excerpt":"We discuss the structure of negacyclic codes of odd length over the ring $\\mathbb{F}_p[u, v]/ \\langle u^2, v^2, uv-vu \\rangle$. We find the unique generating set, the rank and the minimum distance for these negacyclic codes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07431","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":"1501.07431","created_at":"2026-05-18T02:28:21.944629+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.07431v1","created_at":"2026-05-18T02:28:21.944629+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.07431","created_at":"2026-05-18T02:28:21.944629+00:00"},{"alias_kind":"pith_short_12","alias_value":"DPGAPSPMSUW5","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"DPGAPSPMSUW57GNN","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"DPGAPSPM","created_at":"2026-05-18T12:29:17.054201+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/DPGAPSPMSUW57GNN4ZYINQYKHB","json":"https://pith.science/pith/DPGAPSPMSUW57GNN4ZYINQYKHB.json","graph_json":"https://pith.science/api/pith-number/DPGAPSPMSUW57GNN4ZYINQYKHB/graph.json","events_json":"https://pith.science/api/pith-number/DPGAPSPMSUW57GNN4ZYINQYKHB/events.json","paper":"https://pith.science/paper/DPGAPSPM"},"agent_actions":{"view_html":"https://pith.science/pith/DPGAPSPMSUW57GNN4ZYINQYKHB","download_json":"https://pith.science/pith/DPGAPSPMSUW57GNN4ZYINQYKHB.json","view_paper":"https://pith.science/paper/DPGAPSPM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.07431&json=true","fetch_graph":"https://pith.science/api/pith-number/DPGAPSPMSUW57GNN4ZYINQYKHB/graph.json","fetch_events":"https://pith.science/api/pith-number/DPGAPSPMSUW57GNN4ZYINQYKHB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DPGAPSPMSUW57GNN4ZYINQYKHB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DPGAPSPMSUW57GNN4ZYINQYKHB/action/storage_attestation","attest_author":"https://pith.science/pith/DPGAPSPMSUW57GNN4ZYINQYKHB/action/author_attestation","sign_citation":"https://pith.science/pith/DPGAPSPMSUW57GNN4ZYINQYKHB/action/citation_signature","submit_replication":"https://pith.science/pith/DPGAPSPMSUW57GNN4ZYINQYKHB/action/replication_record"}},"created_at":"2026-05-18T02:28:21.944629+00:00","updated_at":"2026-05-18T02:28:21.944629+00:00"}