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This paper presents new fast algorithms for Hermite interpolation andevaluation over finite fields of characteristic two. The algorithms reduce theHermite problems to instances of the standard multipoint interpolation andevaluation problems, which are then solved by existing fast algorithms. Thereductions are simple to implement and free of multiplications, allowing lowoverall multiplicative complexities to be obtained. The algorithms are suitablefor use in encoding and decoding algorithms for multiplicity codes.

Fast Hermite interpolation and evaluation over finite fields of characteristic two