{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:CCF5ISUBLEBCVJDH3HLAUMSU7N","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":"cae9e199b4a06a7b3d9168189e6d926f9081700a805663b6d43bfa38f577d13b","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-03-15T19:48:47Z","title_canon_sha256":"6c3553190fa7b6084e460210d6611f677bce1fff5ea7d359f5c1785b9c06db28"},"schema_version":"1.0","source":{"id":"1903.06779","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.06779","created_at":"2026-05-17T23:51:09Z"},{"alias_kind":"arxiv_version","alias_value":"1903.06779v1","created_at":"2026-05-17T23:51:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.06779","created_at":"2026-05-17T23:51:09Z"},{"alias_kind":"pith_short_12","alias_value":"CCF5ISUBLEBC","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"CCF5ISUBLEBCVJDH","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"CCF5ISUB","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:cc94af0f2283b2512da5e049f68e201623305306134287d786ae154a0a2c737d","target":"graph","created_at":"2026-05-17T23:51:09Z","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":"BCH codes with efficient encoding and decoding algorithms have many applications in communications, cryptography and combinatorics design. This paper studies a class of linear codes of length $ \\frac{q^m-1}{2}$ over $\\mathbb{F}_q$ with special trace representation, where $q$ is an odd prime power. With the help of the inner distributions of some subsets of association schemes from bilinear forms associated with quadratic forms, we determine the weight enumerators of these codes. From determining some cyclotomic coset leaders $\\delta_i$ of cyclotomic cosets modulo $ \\frac{q^m-1}{2}$, we prove t","authors_text":"Chunming Tang, Sihem Mesnager, Xin Ling, Yanfeng Qi","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-03-15T19:48:47Z","title":"A class of narrow-sense BCH codes over $\\mathbb{F}_q$ of length $\\frac{q^m-1}{2}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.06779","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:bf95a3e87db2dc67ea6ce59580f10789374338cd877a57c120062b8193ff433a","target":"record","created_at":"2026-05-17T23:51:09Z","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":"cae9e199b4a06a7b3d9168189e6d926f9081700a805663b6d43bfa38f577d13b","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-03-15T19:48:47Z","title_canon_sha256":"6c3553190fa7b6084e460210d6611f677bce1fff5ea7d359f5c1785b9c06db28"},"schema_version":"1.0","source":{"id":"1903.06779","kind":"arxiv","version":1}},"canonical_sha256":"108bd44a8159022aa467d9d60a3254fb4eade63a4ff688a1f5366047755e5e44","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"108bd44a8159022aa467d9d60a3254fb4eade63a4ff688a1f5366047755e5e44","first_computed_at":"2026-05-17T23:51:09.058735Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:09.058735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hm2aOuAx+actgp5jUCPvv/zBuHHcG0ysYrtT7hSw+RCfylyEELRv7OOBDmHYL06YOWkCyXKyRBCs4UrCMysfBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:09.059236Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.06779","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf95a3e87db2dc67ea6ce59580f10789374338cd877a57c120062b8193ff433a","sha256:cc94af0f2283b2512da5e049f68e201623305306134287d786ae154a0a2c737d"],"state_sha256":"2cf14f2604344478e4ec550d5124db607b333accfabe16da7bdfe4f98423fcfe"}