{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TWZYUJKNTSV7DSOW6VYFBXA7XI","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":"221ac710f700b8f41681d542cf15a1e9edade2127d24394a17b5f05bd31f4708","cross_cats_sorted":["cs.SC","math.AC","math.AG","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-01-30T15:15:37Z","title_canon_sha256":"9f0a04c8be57f2c00475f7904248e272418cb153015377ee7d8a3bf65d52bb73"},"schema_version":"1.0","source":{"id":"1201.6248","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.6248","created_at":"2026-05-18T03:43:52Z"},{"alias_kind":"arxiv_version","alias_value":"1201.6248v4","created_at":"2026-05-18T03:43:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.6248","created_at":"2026-05-18T03:43:52Z"},{"alias_kind":"pith_short_12","alias_value":"TWZYUJKNTSV7","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TWZYUJKNTSV7DSOW","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TWZYUJKN","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:73734fee04cb1a0d3e853a0cd0017b91fe35199bda11d32dd99b8771e6253b49","target":"graph","created_at":"2026-05-18T03:43:52Z","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 generalize the list decoding algorithm for Hermitian codes proposed by Lee and O'Sullivan based on Gr\\\"obner bases to general one-point AG codes, under an assumption weaker than one used by Beelen and Brander. By using the same principle, we also generalize the unique decoding algorithm for one-point AG codes over the Miura-Kamiya $C_{ab}$ curves proposed by Lee, Bras-Amor\\'os and O'Sullivan to general one-point AG codes, without any assumption. Finally we extend the latter unique decoding algorithm to list decoding, modify it so that it can be used with the Feng-Rao improved code construct","authors_text":"Diego Ruano, Olav Geil, Ryutaroh Matsumoto","cross_cats":["cs.SC","math.AC","math.AG","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-01-30T15:15:37Z","title":"List Decoding Algorithms based on Groebner Bases for General One-Point AG Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.6248","kind":"arxiv","version":4},"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":"sha256:4166d69ef23970b29b306ca37ee96904190ee8544b33f4e82461354c2c5d468a","target":"record","created_at":"2026-05-18T03:43:52Z","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":"221ac710f700b8f41681d542cf15a1e9edade2127d24394a17b5f05bd31f4708","cross_cats_sorted":["cs.SC","math.AC","math.AG","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-01-30T15:15:37Z","title_canon_sha256":"9f0a04c8be57f2c00475f7904248e272418cb153015377ee7d8a3bf65d52bb73"},"schema_version":"1.0","source":{"id":"1201.6248","kind":"arxiv","version":4}},"canonical_sha256":"9db38a254d9cabf1c9d6f57050dc1fba0bef0babeea5c1a9d348bb8baf1c778a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9db38a254d9cabf1c9d6f57050dc1fba0bef0babeea5c1a9d348bb8baf1c778a","first_computed_at":"2026-05-18T03:43:52.609296Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:52.609296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eyPL44MYj1o77mvSpVep0wjijVjNPyucNmBXa+Qeog/nZTNVDBrY03SfFzvN3letAO1Xq3xuMOf8LjpVVeAQAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:52.610000Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.6248","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4166d69ef23970b29b306ca37ee96904190ee8544b33f4e82461354c2c5d468a","sha256:73734fee04cb1a0d3e853a0cd0017b91fe35199bda11d32dd99b8771e6253b49"],"state_sha256":"c4be063373a51159fd746ff9b56c7a34450c22c7b802c57b1d7a807a336f82c0"}