Restricted Isometry of Fourier Matrices and List Decodability of Random Linear Codes

@inproceedings{Cheraghchi2013RestrictedIO,
  title={Restricted Isometry of Fourier Matrices and List Decodability of Random Linear Codes},
  author={Mahdi Cheraghchi and Venkatesan Guruswami and Ameya Velingker},
  booktitle={SODA},
  year={2013}
}
@q, with probability arbitrarily close to 1, is list decodable at radius 1--1/q -- e with list size L = O(1/e2) and rate R = Ωq(e2/(log3(1/e))). Up to the polylogarithmic factor in 1/e and constant factors depending on q, this matches the lower bound L = Ωq(1/e2) for the list size and upper bound R = Oq(e2) for the rate. Previously only existence (and not abundance) of such codes was known for the special case q = 2 (Guruswami, Hastad, Sudan and Zuckerman, 2002).In order to obtain our result… 
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