The main computational steps in algebraic soft-decoding, as well as Sudan-type list-decoding, of Reed-Solomon codes are interpolation and factorization. A series of transformations is given for the interpolation problem that arises in these decoding algorithms. These transformations reduce the space and time complexity to a small fraction of the complexity of the original interpolation problem. A factorization procedure that applies directly to the reduced interpolation problem is also presented.
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