{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:KAPIGO4MHDAHDC4CDGOLQTIKCA","short_pith_number":"pith:KAPIGO4M","schema_version":"1.0","canonical_sha256":"501e833b8c38c0718b82199cb84d0a100926a9e65ecaed1d5d57e1159a28eb85","source":{"kind":"arxiv","id":"1607.01887","version":1},"attestation_state":"computed","paper":{"title":"The symbol-pair distance distribution of repeated-root cyclic codes over $\\mathbb{F}_{p^m}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Liqi Wang, Shixin Zhu, Zhonghua Sun","submitted_at":"2016-07-07T06:59:14Z","abstract_excerpt":"Symbol-pair codes are proposed to protect against pair errors in symbol-pair read channels. One of the most important task in symbol-pair coding theory is to determine the minimum pair-distance of symbol-pair codes. In this paper, we investigate the symbol-pair distances of cyclic codes of length $p^e$ over $\\mathbb{F}_{p^m}$. The exact symbol-pair distances of all cyclic codes of such length are determined."},"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":"1607.01887","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-07-07T06:59:14Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"0d82b683cf0e5fb2f4336f239c22d2ae2407a7f61e613e0a10c02618dd301881","abstract_canon_sha256":"15b73d459f9bd8703e4d5df94d1e098064bbe973e4d2dc98f28ee7aa44bef3e2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:23.079481Z","signature_b64":"dfAMwamoOZzh07I97T/lMttc0X5Y35qQj40SkfiOIpoxkUvuncDKT+4oA4MCxTAJMOmJDjO1SQy9q1O2RavpBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"501e833b8c38c0718b82199cb84d0a100926a9e65ecaed1d5d57e1159a28eb85","last_reissued_at":"2026-05-18T01:11:23.079007Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:23.079007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The symbol-pair distance distribution of repeated-root cyclic codes over $\\mathbb{F}_{p^m}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Liqi Wang, Shixin Zhu, Zhonghua Sun","submitted_at":"2016-07-07T06:59:14Z","abstract_excerpt":"Symbol-pair codes are proposed to protect against pair errors in symbol-pair read channels. One of the most important task in symbol-pair coding theory is to determine the minimum pair-distance of symbol-pair codes. In this paper, we investigate the symbol-pair distances of cyclic codes of length $p^e$ over $\\mathbb{F}_{p^m}$. The exact symbol-pair distances of all cyclic codes of such length are determined."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01887","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":"1607.01887","created_at":"2026-05-18T01:11:23.079082+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.01887v1","created_at":"2026-05-18T01:11:23.079082+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.01887","created_at":"2026-05-18T01:11:23.079082+00:00"},{"alias_kind":"pith_short_12","alias_value":"KAPIGO4MHDAH","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"KAPIGO4MHDAHDC4C","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"KAPIGO4M","created_at":"2026-05-18T12:30:25.849896+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/KAPIGO4MHDAHDC4CDGOLQTIKCA","json":"https://pith.science/pith/KAPIGO4MHDAHDC4CDGOLQTIKCA.json","graph_json":"https://pith.science/api/pith-number/KAPIGO4MHDAHDC4CDGOLQTIKCA/graph.json","events_json":"https://pith.science/api/pith-number/KAPIGO4MHDAHDC4CDGOLQTIKCA/events.json","paper":"https://pith.science/paper/KAPIGO4M"},"agent_actions":{"view_html":"https://pith.science/pith/KAPIGO4MHDAHDC4CDGOLQTIKCA","download_json":"https://pith.science/pith/KAPIGO4MHDAHDC4CDGOLQTIKCA.json","view_paper":"https://pith.science/paper/KAPIGO4M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.01887&json=true","fetch_graph":"https://pith.science/api/pith-number/KAPIGO4MHDAHDC4CDGOLQTIKCA/graph.json","fetch_events":"https://pith.science/api/pith-number/KAPIGO4MHDAHDC4CDGOLQTIKCA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KAPIGO4MHDAHDC4CDGOLQTIKCA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KAPIGO4MHDAHDC4CDGOLQTIKCA/action/storage_attestation","attest_author":"https://pith.science/pith/KAPIGO4MHDAHDC4CDGOLQTIKCA/action/author_attestation","sign_citation":"https://pith.science/pith/KAPIGO4MHDAHDC4CDGOLQTIKCA/action/citation_signature","submit_replication":"https://pith.science/pith/KAPIGO4MHDAHDC4CDGOLQTIKCA/action/replication_record"}},"created_at":"2026-05-18T01:11:23.079082+00:00","updated_at":"2026-05-18T01:11:23.079082+00:00"}