{"id":157319,"date":"2010-10-01T00:00:00","date_gmt":"2010-10-01T00:00:00","guid":{"rendered":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/msr-research-item\/a-fourier-analytic-approach-to-reed-muller-decoding\/"},"modified":"2018-10-16T21:56:12","modified_gmt":"2018-10-17T04:56:12","slug":"a-fourier-analytic-approach-to-reed-muller-decoding","status":"publish","type":"msr-research-item","link":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/publication\/a-fourier-analytic-approach-to-reed-muller-decoding\/","title":{"rendered":"A Fourier-analytic approach to Reed-Muller decoding"},"content":{"rendered":"<div class=\"asset-content\">\n<p>We present a Fourier-analytic approach to list-decoding Reed-Muller codes over arbitrary finite fields. We prove that the list-decoding radius for quadratic polynomials equals 1-2\/q over any field F<sub>q<\/sub> where q > 2. This confirms a conjecture due to Gopalan, Klivans and Zuckerman [GKZ08] for degree 2.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We present a Fourier-analytic approach to list-decoding Reed-Muller codes over arbitrary finite fields. We prove that the list-decoding radius for quadratic polynomials equals 1-2\/q over any field Fq where q > 2. This confirms a conjecture due to Gopalan, Klivans and Zuckerman [GKZ08] for degree 2.<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":[{"type":"user_nicename","value":"parik"}],"msr_publishername":"IEEE","msr_publisher_other":"","msr_booktitle":"FOCS 2010","msr_chapter":"","msr_edition":"FOCS 2010","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"\u00a9 2008 IEEE. Personal use of this material is permitted. However, permission to reprint\/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.http:\/\/www.ieee.org\/","msr_conference_name":"FOCS 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