New list decoding algorithms for Reed-Solomon and BCH codes

In this paper we formulate the list decoding of (generalized) Reed-Solomon codes as a rational curve-fitting problem, utilizing the polynomials constructed by the Berlekamp-Massey algorithm. We present a novel list decoding algorithm that corrects up to 1 - root 1 - D errors for (generalized) Reed-Solomon codes, identical to that of the Guruswami-Sudan algorithm which is built upon the Berlekamp-Welch algorithm, where D denote the normalized minimum distance. with appropriate modifications, corrects up to 12 (1 root 1 - 2D) errors for binary BCH codes, which is the best known bound under polynomial complexity. exhibits polynomial complexity in nature, in particular, requires O (n(6)(1 - root 1 - D)(7)) field operations for Reed-Solomon codes in achieving its maximum list error correction capability (n denotes code length), whereas the Guruswami-Sudan algorithm has complexity O(n(10)(1 - D)(4)).