{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:IYZGD66ISNIWF74GMV4DEM72PN","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":"ae97ce989aaa720cb742cd85c400e2ab1a1230dfcd64f7cb610c7b558c3c955e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-23T10:03:36Z","title_canon_sha256":"d04e7dc40d08d4223388627543fc5d27048e35a2fec6073c5c90cb43841d6bdf"},"schema_version":"1.0","source":{"id":"1405.6008","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.6008","created_at":"2026-05-18T02:03:45Z"},{"alias_kind":"arxiv_version","alias_value":"1405.6008v3","created_at":"2026-05-18T02:03:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6008","created_at":"2026-05-18T02:03:45Z"},{"alias_kind":"pith_short_12","alias_value":"IYZGD66ISNIW","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IYZGD66ISNIWF74G","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IYZGD66I","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:d4e2920102e94098a272ff105881c9bbf226b53a5d11c61134fade500486d05d","target":"graph","created_at":"2026-05-18T02:03:45Z","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 the first two sub-quadratic complexity decoding algorithms for one-point Hermitian codes. The first is based on a fast realisation of the Guruswami-Sudan algorithm by using state-of-the-art algorithms from computer algebra for polynomial-ring matrix minimisation. The second is a Power decoding algorithm: an extension of classical key equation decoding which gives a probabilistic decoding algorithm up to the Sudan radius. We show how the resulting key equations can be solved by the same methods from computer algebra, yielding similar asymptotic complexities.","authors_text":"Johan S. R. Nielsen, Peter Beelen","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-23T10:03:36Z","title":"Sub-quadratic Decoding of One-point Hermitian Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6008","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:c6bcb553f381a47b4ba5a46ba7e08b844e030bd54396a7de30f35b1c34517a0d","target":"record","created_at":"2026-05-18T02:03:45Z","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":"ae97ce989aaa720cb742cd85c400e2ab1a1230dfcd64f7cb610c7b558c3c955e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-23T10:03:36Z","title_canon_sha256":"d04e7dc40d08d4223388627543fc5d27048e35a2fec6073c5c90cb43841d6bdf"},"schema_version":"1.0","source":{"id":"1405.6008","kind":"arxiv","version":3}},"canonical_sha256":"463261fbc8935162ff8665783233fa7b7886a84d44bbd7c7319f8714e213c85d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"463261fbc8935162ff8665783233fa7b7886a84d44bbd7c7319f8714e213c85d","first_computed_at":"2026-05-18T02:03:45.368996Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:45.368996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AsetPa/SCkUY2cP8TSAveWMQT1kCKqNFzsMo+36BY7B7rU2wF8sLD8vEvrz2koCUJWgavJlM+T3BR8oml6SyDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:45.369773Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.6008","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c6bcb553f381a47b4ba5a46ba7e08b844e030bd54396a7de30f35b1c34517a0d","sha256:d4e2920102e94098a272ff105881c9bbf226b53a5d11c61134fade500486d05d"],"state_sha256":"9865093f37695d717964798916c9c7a004ba1242cfb3c27f38c1c4f27b2499f1"}