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

Mahdi Cheraghchi, Venkatesan Guruswami, Ameya Velingker

We prove that a random linear code over F_q, with probability arbitrarily close to 1, is list decodable at radius (1-1/q-ε) with list size L=O(1/ε^2) and rate R=Ω_q(ε^2/(log^3(1/ε)…