{"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"}