{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5JXTGDHU6MAJMP7XAA6TVVGUQ6","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":"20fa139c17fbfa63894c5b8bbbeca793b1d994520ba2a280a05681eee6198c9c","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-03-07T15:57:58Z","title_canon_sha256":"60d0cab90020a7b6d1b5b1aa8c8dbe2ad94206128356c9354c83d59ace9767ca"},"schema_version":"1.0","source":{"id":"1803.02731","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.02731","created_at":"2026-05-17T23:57:46Z"},{"alias_kind":"arxiv_version","alias_value":"1803.02731v1","created_at":"2026-05-17T23:57:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.02731","created_at":"2026-05-17T23:57:46Z"},{"alias_kind":"pith_short_12","alias_value":"5JXTGDHU6MAJ","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5JXTGDHU6MAJMP7X","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5JXTGDHU","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:c4a6ce19e86d159e923388312c6c134a2ab9a63cc353c5b0beb273577c8daa66","target":"graph","created_at":"2026-05-17T23:57:46Z","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":"Under research for near sixty years, Bose-$\\!$Ray-$\\!$Chaudhuri-$\\!$Hocquenghem(BCH) codes have played increasingly important roles in many applications such as communication systems, data storage and information security. However, the dimension and minimum distance of BCH codes are seldom solved until now because of their intractable characteristics. The objective of this paper is to study the dimensions of some BCH codes of length $n=2^m+1$ with $m=2t+1$, $4t+2$, $8t+4$ and $m\\geq 10$. Some new techniques are employed to investigate coset leaders modulo $n$. For each type of $m$ above, the f","authors_text":"Liangdong Lu, Qiang Fu, Ruihu Li, Yang Liu, Yi Rao","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-03-07T15:57:58Z","title":"Some binary BCH codes with length $n=2^m+1$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02731","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":"sha256:610acfe97bc2358e426f852cacd8f1d7fd98afc654e6dfe3ad62adb295da8b1b","target":"record","created_at":"2026-05-17T23:57:46Z","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":"20fa139c17fbfa63894c5b8bbbeca793b1d994520ba2a280a05681eee6198c9c","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-03-07T15:57:58Z","title_canon_sha256":"60d0cab90020a7b6d1b5b1aa8c8dbe2ad94206128356c9354c83d59ace9767ca"},"schema_version":"1.0","source":{"id":"1803.02731","kind":"arxiv","version":1}},"canonical_sha256":"ea6f330cf4f300963ff7003d3ad4d4878f0e4b6822e365936e41c871c33b223e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea6f330cf4f300963ff7003d3ad4d4878f0e4b6822e365936e41c871c33b223e","first_computed_at":"2026-05-17T23:57:46.985769Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:46.985769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fMsPL2MXbL2YN4FJ/KauyTK+nBnR8opNrIjSjg3bfcp3KbdzDeY164TirCF8/MQF2UKPPhJ7wPqhOPPgQtmlAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:46.986305Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.02731","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:610acfe97bc2358e426f852cacd8f1d7fd98afc654e6dfe3ad62adb295da8b1b","sha256:c4a6ce19e86d159e923388312c6c134a2ab9a63cc353c5b0beb273577c8daa66"],"state_sha256":"4c3ef704bd9fa7aab1254bac7ece275075c0639f59664eee927d0a98e2267cac"}