{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:YTQFN32HMT4J5PMUPCGRWE3IVA","short_pith_number":"pith:YTQFN32H","schema_version":"1.0","canonical_sha256":"c4e056ef4764f89ebd94788d1b1368a827be3035cd522d25021756594b786583","source":{"kind":"arxiv","id":"1508.00603","version":3},"attestation_state":"computed","paper":{"title":"Efficiently list-decodable punctured Reed-Muller codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.IT"],"primary_cat":"cs.IT","authors_text":"Chaoping Xing, Lingfei Jin, Venkatesan Guruswami","submitted_at":"2015-08-03T21:33:26Z","abstract_excerpt":"The Reed-Muller (RM) code encoding $n$-variate degree-$d$ polynomials over ${\\mathbb F}_q$ for $d < q$, with its evaluation on ${\\mathbb F}_q^n$, has relative distance $1-d/q$ and can be list decoded from a $1-O(\\sqrt{d/q})$ fraction of errors. In this work, for $d \\ll q$, we give a length-efficient puncturing of such codes which (almost) retains the distance and list decodability properties of the Reed-Muller code, but has much better rate. Specificially, when $q =\\Omega( d^2/\\epsilon^2)$, we given an explicit rate $\\Omega\\left(\\frac{\\epsilon}{d!}\\right)$ puncturing of Reed-Muller codes which"},"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":"1508.00603","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-08-03T21:33:26Z","cross_cats_sorted":["cs.CC","math.IT"],"title_canon_sha256":"a1036166262b02ec9a98f1019f3c76708bf58f5aefef5d3497929fce6bf7c009","abstract_canon_sha256":"cc19780ddc116114f822a9d7dde899694415c2240bdeaa87892a62b968149186"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:29.543875Z","signature_b64":"qZkf1mpk0V3wHK28Hq8SykCe1bLSrrNVTX+bwKT0zx+53lt2nfaDK2zYBWqi/z3avTRHBMSpcQQcPSPnH+aCCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4e056ef4764f89ebd94788d1b1368a827be3035cd522d25021756594b786583","last_reissued_at":"2026-05-18T00:47:29.543353Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:29.543353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Efficiently list-decodable punctured Reed-Muller codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.IT"],"primary_cat":"cs.IT","authors_text":"Chaoping Xing, Lingfei Jin, Venkatesan Guruswami","submitted_at":"2015-08-03T21:33:26Z","abstract_excerpt":"The Reed-Muller (RM) code encoding $n$-variate degree-$d$ polynomials over ${\\mathbb F}_q$ for $d < q$, with its evaluation on ${\\mathbb F}_q^n$, has relative distance $1-d/q$ and can be list decoded from a $1-O(\\sqrt{d/q})$ fraction of errors. In this work, for $d \\ll q$, we give a length-efficient puncturing of such codes which (almost) retains the distance and list decodability properties of the Reed-Muller code, but has much better rate. Specificially, when $q =\\Omega( d^2/\\epsilon^2)$, we given an explicit rate $\\Omega\\left(\\frac{\\epsilon}{d!}\\right)$ puncturing of Reed-Muller codes which"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00603","kind":"arxiv","version":3},"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":"1508.00603","created_at":"2026-05-18T00:47:29.543448+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.00603v3","created_at":"2026-05-18T00:47:29.543448+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.00603","created_at":"2026-05-18T00:47:29.543448+00:00"},{"alias_kind":"pith_short_12","alias_value":"YTQFN32HMT4J","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"YTQFN32HMT4J5PMU","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"YTQFN32H","created_at":"2026-05-18T12:29:52.810259+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/YTQFN32HMT4J5PMUPCGRWE3IVA","json":"https://pith.science/pith/YTQFN32HMT4J5PMUPCGRWE3IVA.json","graph_json":"https://pith.science/api/pith-number/YTQFN32HMT4J5PMUPCGRWE3IVA/graph.json","events_json":"https://pith.science/api/pith-number/YTQFN32HMT4J5PMUPCGRWE3IVA/events.json","paper":"https://pith.science/paper/YTQFN32H"},"agent_actions":{"view_html":"https://pith.science/pith/YTQFN32HMT4J5PMUPCGRWE3IVA","download_json":"https://pith.science/pith/YTQFN32HMT4J5PMUPCGRWE3IVA.json","view_paper":"https://pith.science/paper/YTQFN32H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.00603&json=true","fetch_graph":"https://pith.science/api/pith-number/YTQFN32HMT4J5PMUPCGRWE3IVA/graph.json","fetch_events":"https://pith.science/api/pith-number/YTQFN32HMT4J5PMUPCGRWE3IVA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YTQFN32HMT4J5PMUPCGRWE3IVA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YTQFN32HMT4J5PMUPCGRWE3IVA/action/storage_attestation","attest_author":"https://pith.science/pith/YTQFN32HMT4J5PMUPCGRWE3IVA/action/author_attestation","sign_citation":"https://pith.science/pith/YTQFN32HMT4J5PMUPCGRWE3IVA/action/citation_signature","submit_replication":"https://pith.science/pith/YTQFN32HMT4J5PMUPCGRWE3IVA/action/replication_record"}},"created_at":"2026-05-18T00:47:29.543448+00:00","updated_at":"2026-05-18T00:47:29.543448+00:00"}