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

Fast K\"otter-Nielsen-H{\o}holdt Interpolation in the Guruswami-Sudan Algorithm