{"paper":{"title":"List Decodability at Small Radii","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Gennian Ge, Jianxing Yin, Lijun Ji, San Ling, Yeow Meng Chee","submitted_at":"2010-10-16T03:44:07Z","abstract_excerpt":"$A'(n,d,e)$, the smallest $\\ell$ for which every binary error-correcting code of length $n$ and minimum distance $d$ is decodable with a list of size $\\ell$ up to radius $e$, is determined for all $d\\geq 2e-3$. As a result, $A'(n,d,e)$ is determined for all $e\\leq 4$, except for 42 values of $n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3312","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"}