A Fourier-analytic approach to Reed-Muller decoding

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_q where q > 2. This confirms a conjecture due to Gopalan, Klivans and Zuckerman [GKZ08] for degree 2.

Quadratic-Aug 4th.pdf
PDF file

In  FOCS 2010

Publisher  IEEE
© 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/

Details

TypeInproceedings
> Publications > A Fourier-analytic approach to Reed-Muller decoding