List Decoding of Generalized Reed–Solomon Codes Over Commutative Rings

Abstract

We show that the list decoding procedure of Guruswami and Sudan may be used to decode generalized Reed-Solomon (RS) codes defined over commutative rings with identity. An algorithm for performing the first of the two phases of this decoding procedure is also given. In particular, we show that for generalized RS codes over chain rings, the probability of picking an incorrect codeword from a given list can be reduced by increasing the size of the code alphabet while keeping the length and minimum (Hamming) distance of the code constant