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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1207.1140","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-04T23:21:09Z","cross_cats_sorted":["math.CO","math.IT","math.PR"],"title_canon_sha256":"91276862bcd0a918701b51c1da1b49e527d8d3a08f858353a4b95739ec7bc4ed","abstract_canon_sha256":"0d9a9c09586406a60b279bea8dbc95d6567ceae6cd07247ce2f4b67c0842716c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:46.773853Z","signature_b64":"Q7C6m30vJNaYv6vvSfQBbsgHMPkGWmczF9D2VJZ46IuKJ9hzx1Wu/aGJmN0I8d/AzoPBuXx58OjczP4ELi5dDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23fe12cc5f0c6decaf34f9e9f82c5d8569d43a7bd078aef10f649e616782dbd6","last_reissued_at":"2026-05-18T03:51:46.773349Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:46.773349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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))). 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