{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:65PW27AXDHCUQNLEK6ZJ7XX4U3","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":"57f55216978db1c6ddf0777761f387f3ccc57d8b2ee878ebd56b45d2fb76f3ff","cross_cats_sorted":["cs.DS","math.AG","math.IT","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-04-18T21:02:36Z","title_canon_sha256":"a24e41d3f2a405658726c39cc781f4347fe02ab396b4525401fc007c02f139eb"},"schema_version":"1.0","source":{"id":"1204.4209","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.4209","created_at":"2026-05-18T02:21:16Z"},{"alias_kind":"arxiv_version","alias_value":"1204.4209v1","created_at":"2026-05-18T02:21:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.4209","created_at":"2026-05-18T02:21:16Z"},{"alias_kind":"pith_short_12","alias_value":"65PW27AXDHCU","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"65PW27AXDHCUQNLE","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"65PW27AX","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:4b44503f8abc74d034f76ea8e63e9a3352805ae805eab447b620aaf1ef255fb1","target":"graph","created_at":"2026-05-18T02:21:16Z","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 give a new construction of algebraic codes which are efficiently list decodable from a fraction $1-R-\\eps$ of adversarial errors where $R$ is the rate of the code, for any desired positive constant $\\eps$. The worst-case list size output by the algorithm is $O(1/\\eps)$, matching the existential bound for random codes up to constant factors. Further, the alphabet size of the codes is a constant depending only on $\\eps$ - it can be made $\\exp(\\tilde{O}(1/\\eps^2))$ which is not much worse than the lower bound of $\\exp(\\Omega(1/\\eps))$. The parameters we achieve are thus quite close to the exis","authors_text":"Chaoping Xing, Venkatesan Guruswami","cross_cats":["cs.DS","math.AG","math.IT","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-04-18T21:02:36Z","title":"Folded Codes from Function Field Towers and Improved Optimal Rate List Decoding"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4209","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:f8fb6eeea757649973db20979faf149538e3a0944f6789bc5c58fa5a2c957511","target":"record","created_at":"2026-05-18T02:21:16Z","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":"57f55216978db1c6ddf0777761f387f3ccc57d8b2ee878ebd56b45d2fb76f3ff","cross_cats_sorted":["cs.DS","math.AG","math.IT","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-04-18T21:02:36Z","title_canon_sha256":"a24e41d3f2a405658726c39cc781f4347fe02ab396b4525401fc007c02f139eb"},"schema_version":"1.0","source":{"id":"1204.4209","kind":"arxiv","version":1}},"canonical_sha256":"f75f6d7c1719c548356457b29fdefca6df5efaca43cd58a1c8b6cbcf9ad8a867","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f75f6d7c1719c548356457b29fdefca6df5efaca43cd58a1c8b6cbcf9ad8a867","first_computed_at":"2026-05-18T02:21:16.173752Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:16.173752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iU5vrU8D6hyziegrcbo/KeUDoUMwEXACcgJZarznwF8RaDXuurnjdvNvCDv6KQPUfatMiO7Kv/bRxf6RqiZgBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:16.174391Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.4209","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8fb6eeea757649973db20979faf149538e3a0944f6789bc5c58fa5a2c957511","sha256:4b44503f8abc74d034f76ea8e63e9a3352805ae805eab447b620aaf1ef255fb1"],"state_sha256":"0b48c6739693565f48300d847cc0df4e4b4c5157051230f0d6c00341f2938503"}