{"paper":{"title":"Explicit Codes Achieving List Decoding Capacity: Error-correction with Optimal Redundancy","license":"","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Atri Rudra, Venkatesan Guruswami","submitted_at":"2005-11-18T22:31:44Z","abstract_excerpt":"We present error-correcting codes that achieve the information-theoretically best possible trade-off between the rate and error-correction radius. Specifically, for every $0 < R < 1$ and $\\eps> 0$, we present an explicit construction of error-correcting codes of rate $R$ that can be list decoded in polynomial time up to a fraction $(1-R-\\eps)$ of {\\em worst-case} errors. At least theoretically, this meets one of the central challenges in algorithmic coding theory.\n  Our codes are simple to describe: they are {\\em folded Reed-Solomon codes}, which are in fact {\\em exactly} Reed-Solomon (RS) cod"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0511072","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/cs/0511072/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"}