{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:C65DWT7YZ255RO7WELZ5L5E55U","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":"d68b62a9b13ec76a2fe666cf6114bc63215b0dc1de4b7ca2c5d8ec19b4726f34","cross_cats_sorted":["math.AC","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-07-11T13:40:19Z","title_canon_sha256":"dfb9cc0ac9443f421988f99897347b762839bf115e9f409c3231be437b648f4a"},"schema_version":"1.0","source":{"id":"1307.3107","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.3107","created_at":"2026-05-18T03:17:44Z"},{"alias_kind":"arxiv_version","alias_value":"1307.3107v2","created_at":"2026-05-18T03:17:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3107","created_at":"2026-05-18T03:17:44Z"},{"alias_kind":"pith_short_12","alias_value":"C65DWT7YZ255","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"C65DWT7YZ255RO7W","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"C65DWT7Y","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:adbf5062ebd5e270f6669828dc294e5d248268de6698d1d72289b000df44de9d","target":"graph","created_at":"2026-05-18T03:17:44Z","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":"We present a new bound for the minimum distance of a general primary linear code. For affine variety codes defined from generalised C_{ab} curves the new bound often improves dramatically on the Feng-Rao bound for primary codes. The method does not only work for the minimum distance but can be applied to any generalised Hamming weight","authors_text":"Olav Geil, Stefano Martin","cross_cats":["math.AC","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-07-11T13:40:19Z","title":"An improvement of the Feng-Rao bound for primary codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3107","kind":"arxiv","version":2},"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":"sha256:002e57391a80110d7ae8e4b8a4c3f5c91e30d65185d9f9f05fd57651d57be201","target":"record","created_at":"2026-05-18T03:17:44Z","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":"d68b62a9b13ec76a2fe666cf6114bc63215b0dc1de4b7ca2c5d8ec19b4726f34","cross_cats_sorted":["math.AC","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-07-11T13:40:19Z","title_canon_sha256":"dfb9cc0ac9443f421988f99897347b762839bf115e9f409c3231be437b648f4a"},"schema_version":"1.0","source":{"id":"1307.3107","kind":"arxiv","version":2}},"canonical_sha256":"17ba3b4ff8cebbd8bbf622f3d5f49ded2fb49a5516e314362ffa5a580076ae5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17ba3b4ff8cebbd8bbf622f3d5f49ded2fb49a5516e314362ffa5a580076ae5c","first_computed_at":"2026-05-18T03:17:44.035157Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:44.035157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jSyyA5Boa2MvJ3wZaURJLDDzLVCQIahZ+Je3BuqUz3FdoDfDm9Iz9gh1qQWezGdMWyEIY13lvuTPj1Xnl7jiAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:44.035720Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.3107","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:002e57391a80110d7ae8e4b8a4c3f5c91e30d65185d9f9f05fd57651d57be201","sha256:adbf5062ebd5e270f6669828dc294e5d248268de6698d1d72289b000df44de9d"],"state_sha256":"6c295c95e875d3ea97c50fe3e70d37d4f1aeb567d29aea5d57a0ba4bd9c30796"}