Patent ID: 6915478

Claim:
A method of determining error magnitudes in Reed-Solomon decoding, wherein a vector of v syndromes E i 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 E l = ∑ j = 1 v ⁢ ⁢ ⅇ l j ⁢ a i ⁢ ⁢ l j , where a is a primitive of the codeword, comprising the steps of: 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=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=W having a single unknown that can be solved for a respective error magnitude.