Fast Kötter-Nielsen-Høholdt Interpolation in the Guruswami-Sudan Algorithm

Abstract: The K\"otter-Nielsen-H{\o}holdt algorithm is a popular way to construct the bivariate interpolation polynomial in the Guruswami-Sudan decoding algorithm for Reed-Solomon codes. In this paper, we show how one can use Divide & Conquer techniques to provide an asymptotic speed-up of the algorithm, rendering its complexity quasi-linear in n. Several of our observations can also provide a practical speed-up to the classical version of the algorithm.