1. A method of determining error magnitudes in Reed-Solomon decoding, wherein a vector of v syndromes E l and v error locations l j are determined from a received codeword, and error magnitudes e l j at the v error locations can be determined from the equation 21 E l = &Sum; j = 1 v &it; &it; &ee; l j &it; a i &it; &it; l j, triangularizing a v×v Vandermonde matrix of the elements a il j to generate elements of a matrix V; generating a syndrome vector W of syndromes E i, adjusted for the triangularization of matrix V; generating a solution to an equation of a form Vx M&equals;W, where M is a vector of the error magnitudes e l j and Vx is a vector of matrix V, having a single unknown error magnitude; substituting to create other equations of the form Vx M&equals;W having a single unknown that can be solved for a respective error magnitude.