{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:6KLCOVC63CSKDFGILCDSYSLLSO","short_pith_number":"pith:6KLCOVC6","schema_version":"1.0","canonical_sha256":"f29627545ed8a4a194c858872c496b938d4364233ab1f012e9b5cac102035036","source":{"kind":"arxiv","id":"1407.3433","version":2},"attestation_state":"computed","paper":{"title":"List decoding Reed-Muller codes over small fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.CC","authors_text":"Abhishek Bhowmick, Shachar Lovett","submitted_at":"2014-07-13T05:47:07Z","abstract_excerpt":"The list decoding problem for a code asks for the maximal radius up to which any ball of that radius contains only a constant number of codewords. The list decoding radius is not well understood even for well studied codes, like Reed-Solomon or Reed-Muller codes.\n  Fix a finite field $\\mathbb{F}$. The Reed-Muller code $\\mathrm{RM}_{\\mathbb{F}}(n,d)$ is defined by $n$-variate degree-$d$ polynomials over $\\mathbb{F}$. In this work, we study the list decoding radius of Reed-Muller codes over a constant prime field $\\mathbb{F}=\\mathbb{F}_p$, constant degree $d$ and large $n$. We show that the list"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1407.3433","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-07-13T05:47:07Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"fbf649a4236d215016f2fa557a39599685620458dd1f516f2a223bc03fa8cf01","abstract_canon_sha256":"c6a7c4850dc41d982ece40c2031aa182f7e2ddac646ece01259ea5686b4ae4c8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:23.912499Z","signature_b64":"LyHjDt8QjfREHX5JUEvhIiaXbppoJI6Ub9M51NMkVIFMhtFmH5eYzOuYLP83plv4nTY32VpkIDv1zrE+NzraBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f29627545ed8a4a194c858872c496b938d4364233ab1f012e9b5cac102035036","last_reissued_at":"2026-05-18T02:47:23.912111Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:23.912111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"List decoding Reed-Muller codes over small fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.CC","authors_text":"Abhishek Bhowmick, Shachar Lovett","submitted_at":"2014-07-13T05:47:07Z","abstract_excerpt":"The list decoding problem for a code asks for the maximal radius up to which any ball of that radius contains only a constant number of codewords. The list decoding radius is not well understood even for well studied codes, like Reed-Solomon or Reed-Muller codes.\n  Fix a finite field $\\mathbb{F}$. The Reed-Muller code $\\mathrm{RM}_{\\mathbb{F}}(n,d)$ is defined by $n$-variate degree-$d$ polynomials over $\\mathbb{F}$. In this work, we study the list decoding radius of Reed-Muller codes over a constant prime field $\\mathbb{F}=\\mathbb{F}_p$, constant degree $d$ and large $n$. We show that the list"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3433","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1407.3433","created_at":"2026-05-18T02:47:23.912168+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.3433v2","created_at":"2026-05-18T02:47:23.912168+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.3433","created_at":"2026-05-18T02:47:23.912168+00:00"},{"alias_kind":"pith_short_12","alias_value":"6KLCOVC63CSK","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"6KLCOVC63CSKDFGI","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"6KLCOVC6","created_at":"2026-05-18T12:28:16.859392+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6KLCOVC63CSKDFGILCDSYSLLSO","json":"https://pith.science/pith/6KLCOVC63CSKDFGILCDSYSLLSO.json","graph_json":"https://pith.science/api/pith-number/6KLCOVC63CSKDFGILCDSYSLLSO/graph.json","events_json":"https://pith.science/api/pith-number/6KLCOVC63CSKDFGILCDSYSLLSO/events.json","paper":"https://pith.science/paper/6KLCOVC6"},"agent_actions":{"view_html":"https://pith.science/pith/6KLCOVC63CSKDFGILCDSYSLLSO","download_json":"https://pith.science/pith/6KLCOVC63CSKDFGILCDSYSLLSO.json","view_paper":"https://pith.science/paper/6KLCOVC6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.3433&json=true","fetch_graph":"https://pith.science/api/pith-number/6KLCOVC63CSKDFGILCDSYSLLSO/graph.json","fetch_events":"https://pith.science/api/pith-number/6KLCOVC63CSKDFGILCDSYSLLSO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6KLCOVC63CSKDFGILCDSYSLLSO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6KLCOVC63CSKDFGILCDSYSLLSO/action/storage_attestation","attest_author":"https://pith.science/pith/6KLCOVC63CSKDFGILCDSYSLLSO/action/author_attestation","sign_citation":"https://pith.science/pith/6KLCOVC63CSKDFGILCDSYSLLSO/action/citation_signature","submit_replication":"https://pith.science/pith/6KLCOVC63CSKDFGILCDSYSLLSO/action/replication_record"}},"created_at":"2026-05-18T02:47:23.912168+00:00","updated_at":"2026-05-18T02:47:23.912168+00:00"}