Les codes de Reed Solomon: étude et simulation.

Abstract—In this paper we study generalized Reed-Solomon codes (GRS codes) over commutative, noncommutative rings, show that the classical Welch-Berlekamp and Guruswami-Sudan

Sala, “A New Bound for the Minimum Distance of a Cyclic Code From Its Defining Set,” Information Theory, IEEE Transactions on, vol.. Tzeng, “A new procedure for decoding cyclic and

Our approach is based on the notion of a left module Gr¨ obner basis in iterated skew polynomial rings2.

Abstract An iterated refinement procedure for the Guruswami–Sudan list decoding algorithm for Generalised Reed–Solomon codes based on Alekhnovich’s module min- imisation is

I N 1999, Guruswami and Sudan [3]–[5] extended Sudan’s original approach [6] by introducing multiplicities in the interpolation step of their polynomial-time list decoding pro-

Abstract An iterated refinement procedure for the Guruswami–Sudan list decoding algorithm for Generalised Reed–Solomon codes based on Alekhnovich’s module min- imisation is

The motivation was a fast realization of the interpolation problem of the Guruswami-Sudan principle, where the block Hankel structure of the set of linear homogeneous equations

The fastest known algorithms for computing discrete logarithms in a finite field F p n all rely on variants of the number field sieve or the function field sieve.. Some