Efficient List-Decoding of Reed-Solomon Codes with the Fundamental Iterative Algorithm

In this paper we propose a new algorithm that solves the Guruswami-Sudan interpolation step for Reed-Solomon codes efficiently. It is a generalization of the Feng-Tzeng approach, the so-called Fundamental Iterative Algorithm. From the interpolation constraints of the Guruswami-Sudan principle it is well known that an improvement of the decoding radius can only be achieved, if the multiplicity parameter s is smaller than the list size l. The code length is n and our proposed algorithm has a complexity (without asymptotic assumptions) of O (ls(4)n(2)).