{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LTH3Y5B3DRFJ377GMU7OYD4TAB","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":"40625455eec90ac3536db8386f58a2cdae9016385dc3d6f512d913380006216e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-10-25T01:44:36Z","title_canon_sha256":"45d274364054aef8401bfd4eac0178d7ab6eab758d288da04d0023db3145e309"},"schema_version":"1.0","source":{"id":"1210.6722","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.6722","created_at":"2026-05-18T03:27:32Z"},{"alias_kind":"arxiv_version","alias_value":"1210.6722v3","created_at":"2026-05-18T03:27:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.6722","created_at":"2026-05-18T03:27:32Z"},{"alias_kind":"pith_short_12","alias_value":"LTH3Y5B3DRFJ","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LTH3Y5B3DRFJ377G","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LTH3Y5B3","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:aa0567847949fa9ff7d3537a9382e566bdf200ee43e3da1d2208d970ae0b4e05","target":"graph","created_at":"2026-05-18T03:27:32Z","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 show that the Feng-Rao bound for dual codes and a similar bound by Andersen and Geil [H.E. Andersen and O. Geil, Evaluation codes from order domain theory, Finite Fields Appl., 14 (2008), pp. 92-123] for primary codes are consequences of each other. This implies that the Feng-Rao decoding algorithm can be applied to decode primary codes up to half their designed minimum distance. The technique applies to any linear code for which information on well-behaving pairs is available. Consequently we are able to decode efficiently a large class of codes for which no non-trivial decoding algorithm ","authors_text":"Diego Ruano, Olav Geil, Ryutaroh Matsumoto","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-10-25T01:44:36Z","title":"Feng-Rao decoding of primary codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6722","kind":"arxiv","version":3},"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:ee705dd941ed67faf2d4d824e7c473c42e28dd9306e8705430ede27b767bcee2","target":"record","created_at":"2026-05-18T03:27:32Z","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":"40625455eec90ac3536db8386f58a2cdae9016385dc3d6f512d913380006216e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-10-25T01:44:36Z","title_canon_sha256":"45d274364054aef8401bfd4eac0178d7ab6eab758d288da04d0023db3145e309"},"schema_version":"1.0","source":{"id":"1210.6722","kind":"arxiv","version":3}},"canonical_sha256":"5ccfbc743b1c4a9dffe6653eec0f930045100d9f649dd6ca05f88a3b479ce090","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ccfbc743b1c4a9dffe6653eec0f930045100d9f649dd6ca05f88a3b479ce090","first_computed_at":"2026-05-18T03:27:32.526822Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:32.526822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WEVKJb0iQC0p6CaVkljIdhingoR+1WAQ/QrfWBftxSEgdCnwxMDNZIoQU1AUbZSgomQjT77HpjmMwwXIvNqqAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:32.527305Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.6722","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee705dd941ed67faf2d4d824e7c473c42e28dd9306e8705430ede27b767bcee2","sha256:aa0567847949fa9ff7d3537a9382e566bdf200ee43e3da1d2208d970ae0b4e05"],"state_sha256":"b9d6ece6e199d3576ea5c9624f27d72c0e4a4da93c04f4c091db4208ee8bc932"}