{"paper":{"title":"Optimal rate algebraic list decoding using narrow ray class fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.IT","math.IT"],"primary_cat":"math.NT","authors_text":"Chaoping Xing, Venkatesan Guruswami","submitted_at":"2013-02-27T04:38:18Z","abstract_excerpt":"We use class field theory, specifically Drinfeld modules of rank 1, to construct a family of asymptotically good algebraic-geometric (AG) codes over fixed alphabets. Over a field of size $\\ell^2$, these codes are within $2/(\\sqrt{\\ell}-1)$ of the Singleton bound. The functions fields underlying these codes are subfields with a cyclic Galois group of the narrow ray class field of certain function fields. The resulting codes are \"folded\" using a generator of the Galois group. This generalizes earlier work by the first author on folded AG codes based on cyclotomic function fields. Using the Chebo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6660","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"}