{"paper":{"title":"Every list-decodable code for high noise has abundant near-optimal rate puncturings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Atri Rudra, Mary Wootters","submitted_at":"2013-10-07T19:18:51Z","abstract_excerpt":"We show that any q-ary code with sufficiently good distance can be randomly punctured to obtain, with high probability, a code that is list decodable up to radius $1 - 1/q - \\epsilon$ with near-optimal rate and list sizes. Our results imply that \"most\" Reed-Solomon codes are list decodable beyond the Johnson bound, settling the long-standing open question of whether any Reed Solomon codes meet this criterion.\n  More precisely, we show that a Reed-Solomon code with random evaluation points is, with high probability, list decodable up to radius $1 - \\epsilon$ with list sizes $O(1/\\epsilon)$ and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1891","kind":"arxiv","version":1},"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"}