Fast rational interpolation, Reed-Solomon decoding, and the linear complexity profiles of sequences

An asymptotically fast algorithm for solving the generalized rational interpolation problem is presented. This problem has been studied as part of system theory and is related to the solution of the classical and Welch-Berlekamp (1983) key equations which arise in Reed-Solomon decoding. The algorithm can also be used to compute the linear complexity profile of a binary sequence of length m using only O(m(log m)/sup 2/ log log m) bit operations.