{"paper":{"title":"Folded Codes from Function Field Towers and Improved Optimal Rate List Decoding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.AG","math.IT","math.NT"],"primary_cat":"cs.IT","authors_text":"Chaoping Xing, Venkatesan Guruswami","submitted_at":"2012-04-18T21:02:36Z","abstract_excerpt":"We give a new construction of algebraic codes which are efficiently list decodable from a fraction $1-R-\\eps$ of adversarial errors where $R$ is the rate of the code, for any desired positive constant $\\eps$. The worst-case list size output by the algorithm is $O(1/\\eps)$, matching the existential bound for random codes up to constant factors. Further, the alphabet size of the codes is a constant depending only on $\\eps$ - it can be made $\\exp(\\tilde{O}(1/\\eps^2))$ which is not much worse than the lower bound of $\\exp(\\Omega(1/\\eps))$. The parameters we achieve are thus quite close to the exis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4209","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"}