{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GKURJTOJICUWHJAEOVRT6BCBT6","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"955ce322f0e27b5941a177501acf5fc388eed6165d0773f0ba24075655460a4c","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-21T02:03:49Z","title_canon_sha256":"6c47a22856f0803f2e7519011f7fc1d0369dc2a8e8f4d13dccfe9a04cea188bb"},"schema_version":"1.0","source":{"id":"1405.5278","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.5278","created_at":"2026-05-18T02:51:24Z"},{"alias_kind":"arxiv_version","alias_value":"1405.5278v1","created_at":"2026-05-18T02:51:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.5278","created_at":"2026-05-18T02:51:24Z"},{"alias_kind":"pith_short_12","alias_value":"GKURJTOJICUW","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GKURJTOJICUWHJAE","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GKURJTOJ","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:0df40885bddfa26ca58605a304c60216842cbc20d5c5b45732ada0f80d14f7de","target":"graph","created_at":"2026-05-18T02:51:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let m, k be positive integers, p be an odd prime and $\\pi $ be a primitive element of $\\mathbb{F}_{p^m}$. In this paper, we determine the weight distribution of a family of cyclic codes $\\mathcal{C}_t$ over $\\mathbb{F}_p$, whose duals have two zeros $\\pi^{-t}$ and $-\\pi^{-t}$, where $t$ satisfies $t\\equiv \\frac{p^k+1}{2}p^\\tau \\ ({\\rm mod}\\ \\frac{p^m-1}{2}) $ for some $\\tau \\in \\{0,1,\\cdots, m-1\\}$.","authors_text":"Hongwei Liu, Long Yu","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-21T02:03:49Z","title":"The weight distribution of a family of p-ary cyclic codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5278","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:21f1516d5e769f219125e2ff768e03a7df37fd36dfc5eb17a1976527241024eb","target":"record","created_at":"2026-05-18T02:51:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"955ce322f0e27b5941a177501acf5fc388eed6165d0773f0ba24075655460a4c","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-21T02:03:49Z","title_canon_sha256":"6c47a22856f0803f2e7519011f7fc1d0369dc2a8e8f4d13dccfe9a04cea188bb"},"schema_version":"1.0","source":{"id":"1405.5278","kind":"arxiv","version":1}},"canonical_sha256":"32a914cdc940a963a40475633f04419f8c42f5ccf50dd0236fd4f72f8b8cfefd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32a914cdc940a963a40475633f04419f8c42f5ccf50dd0236fd4f72f8b8cfefd","first_computed_at":"2026-05-18T02:51:24.620961Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:24.620961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ee5j1Mrz2c8A69gmHM5CnYrLr8doiB9XamtJEJfJZZu/qFT8IG+L2TrdcoyNlIUPAUklv9Ypu6DpA1gNJBThCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:24.621555Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.5278","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21f1516d5e769f219125e2ff768e03a7df37fd36dfc5eb17a1976527241024eb","sha256:0df40885bddfa26ca58605a304c60216842cbc20d5c5b45732ada0f80d14f7de"],"state_sha256":"8b2f8bf9b380d569b8af4f72c7a0eb8a9361f2f86d367d340174913c5789ec42"}