Algebraic Soft- and Hard-Decision Decoding of Generalized Reed--Solomon and Cyclic Codes

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

In this section, we formulate the decoding of an RS(n, k) code virtually extended to a VIRS (n, k, s) code as a modified GS interpolation problem.. The constraints of the

In our contribution we use FT’s Euclidean algorithm to de- code Interleaved Reed–Solomon (IRS) codes ([7], [8]), more specifically a virtual extension to an IRS code that has

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

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