{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:EGIHQFIVCLS4G74GWB3SRBJSDK","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":"5485a8a270b873f49ff2acdd4eba0c6d3ebab2a93cd0a858c3e8b39b3f10ef8a","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2022-07-05T08:18:46Z","title_canon_sha256":"a4b1506532760d1d81ca193a4321fa57017ed382a370c988a4a4608b6d5c4f4f"},"schema_version":"1.0","source":{"id":"2207.01877","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.01877","created_at":"2026-07-05T04:37:45Z"},{"alias_kind":"arxiv_version","alias_value":"2207.01877v1","created_at":"2026-07-05T04:37:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.01877","created_at":"2026-07-05T04:37:45Z"},{"alias_kind":"pith_short_12","alias_value":"EGIHQFIVCLS4","created_at":"2026-07-05T04:37:45Z"},{"alias_kind":"pith_short_16","alias_value":"EGIHQFIVCLS4G74G","created_at":"2026-07-05T04:37:45Z"},{"alias_kind":"pith_short_8","alias_value":"EGIHQFIV","created_at":"2026-07-05T04:37:45Z"}],"graph_snapshots":[{"event_id":"sha256:cd51300a8d582b06de1da26d73776cb1b5c02b6343dba1cae1e704a5b7b70a6e","target":"graph","created_at":"2026-07-05T04:37:45Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2207.01877/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Negacyclic BCH codes are a subclass of neagcyclic codes and are the best linear codes in many cases. However, there have been very few results on negacyclic BCH codes. Let $q$ be an odd prime power and $m$ be a positive integer. The objective of this paper is to study negacyclic BCH codes with length $\\frac{q^m-1}{2}$ and $\\frac{q^m+1}{2}$ over the finite field $\\mathbf(q)$ and analyse their parameters. The negacyclic BCH codes presented in this paper have good parameters in general, and contain many optimal linear codes. For certain $q$ and $m$, compared with cyclic codes with the same dimens","authors_text":"Cunsheng Ding, Xiaoqiang Wang, Zhonghua Sun","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2022-07-05T08:18:46Z","title":"Two families of negacyclic BCH codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.01877","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":"sha256:6d2c3921c480e7d9908c11bcce3442c22cdaa09ea2a932e67ff8a30e3e7e09f1","target":"record","created_at":"2026-07-05T04:37:45Z","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":"5485a8a270b873f49ff2acdd4eba0c6d3ebab2a93cd0a858c3e8b39b3f10ef8a","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2022-07-05T08:18:46Z","title_canon_sha256":"a4b1506532760d1d81ca193a4321fa57017ed382a370c988a4a4608b6d5c4f4f"},"schema_version":"1.0","source":{"id":"2207.01877","kind":"arxiv","version":1}},"canonical_sha256":"219078151512e5c37f86b0772885321a91e9a9ce0d905f897c0383dc833fba9f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"219078151512e5c37f86b0772885321a91e9a9ce0d905f897c0383dc833fba9f","first_computed_at":"2026-07-05T04:37:45.355713Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:37:45.355713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dTf4hx5ThdIpAnocrLXad/My9a9YzolwDP0RSq8G8OORd8EPKANN7IiUNoaJi0DAzrcSvI9OhLGLNbwTSAFSAg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:37:45.356110Z","signed_message":"canonical_sha256_bytes"},"source_id":"2207.01877","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d2c3921c480e7d9908c11bcce3442c22cdaa09ea2a932e67ff8a30e3e7e09f1","sha256:cd51300a8d582b06de1da26d73776cb1b5c02b6343dba1cae1e704a5b7b70a6e"],"state_sha256":"1014a6ac6de89e2b2f7aab147523e27d3dd3efc1818a9fa86df0995f8df869a8"}