{"paper":{"title":"Improved List-Decodability of Reed--Solomon Codes via Tree Packings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Chong Shangguan, Itzhak Tamo, Mary Wootters, Ray Li, Zeyu Guo","submitted_at":"2020-11-09T14:22:37Z","abstract_excerpt":"This paper shows that there exist Reed--Solomon (RS) codes, over \\black{exponentially} large finite fields \\black{in the code length}, that are combinatorially list-decodable well beyond the Johnson radius, in fact almost achieving the list-decoding capacity.\n  In particular, we show that for any $\\epsilon\\in (0,1]$ there exist RS codes with rate $\\Omega(\\frac{\\epsilon}{\\log(1/\\epsilon)+1})$ that are list-decodable from radius of $1-\\epsilon$. We generalize this result to list-recovery, showing that there exist $(1 - \\epsilon, \\ell, O(\\ell/\\epsilon))$-list-recoverable RS codes with rate $\\Omeg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.04453","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2011.04453/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}