{"paper":{"title":"Restricted Isometry of Fourier Matrices and List Decodability of Random Linear Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT","math.PR"],"primary_cat":"cs.IT","authors_text":"Ameya Velingker, Mahdi Cheraghchi, Venkatesan Guruswami","submitted_at":"2012-07-04T23:21:09Z","abstract_excerpt":"We prove that a random linear code over F_q, with probability arbitrarily close to 1, is list decodable at radius (1-1/q-\\epsilon) with list size L=O(1/\\epsilon^2) and rate R=\\Omega_q(\\epsilon^2/(log^3(1/\\epsilon))). Up to the polylogarithmic factor in (1/\\epsilon) and constant factors depending on q, this matches the lower bound L=\\Omega_q(1/\\epsilon^2) for the list size and upper bound R=O_q(\\epsilon^2) for the rate. Previously only existence (and not abundance) of such codes was known for the special case q=2 (Guruswami, H{\\aa}stad, Sudan and Zuckerman, 2002).\n  In order to obtain our resul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1140","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"}