Simultaneous Partial Inverses and Decoding Interleaved Reed-Solomon Codes

This paper introduces the simultaneous partialinverse problem for polynomials and develops its application to decoding interleaved Reed-Solomon codes and subfield-evaluation codes beyond half the minimum distance. The simultaneous partial-inverse problem has a unique solution (up to a scale factor), which can be computed by an efficient new algorithm, for which we also offer some variations. Decoding interleaved ReedSolomon codes and subfield-evaluation codes (beyond half the minimum distance) can be reduced to the simultaneous partialinverse problem, and pertinent decoding algorithms are obtained by easy adaptions of the simultaneous partial-inverse algorithms. The resulting unique-decoding algorithms are new and efficient, and they have state-of-the-art decoding capability.