Grobner basis view of Welch-Berlekamp algorithm for Reed-Solomon codes

Grobner bases of modules have been used to provide a unifying theoretical approach to the various algorithms for solving the key equation Ω(x)≡S(x)Λ(x) (mod X^2f) in decoding Reed-Solomon codes. The Welch-Berlekamp algorithm solves a different key equation based on rational interpolation. When the solution is viewed as a canonical element in a module M, the algorithm is developed by considering Grobner bases with respect to different term orders