On Fractional Decoding of Reed-Solomon Codes

Abstract

We define a virtual projection of a Reed-Solomon code $RS(q^l,n,k)$ to an $RS(q,n,k)$ Reed-Solomon code. A new probabilistic decoding algorithm that can be used to perform fractional decoding beyond the $\alpha$- decoding radius is considered. An upper bound for the failure probability of the new algorithm is given, and the performance is illustrated by examples.