Patent ID: 6345376
Filing Date: 2002-02-05
Classification: H03M

Abstract:
A machine-implementable method for correcting up to t errors in words defined over a linear cyclic code and received from a communications subsystem or read back from a storage subsystem or the like, said code having up to a maximum number of consecutive zero or null values occurring in said code definition, each received word being subject to separate processing for location and value of errors, comprising the steps of:(a) deriving one or more syndromes from each received word and computing an error locator polynomial Æ’(z) of degree t from the derived syndromes; (b) mapping Æ’(z) into a canonical form as an augmented matrix M of a system of m linear simultaneous equations in a finite Galois field GF(2m); (c) extracting at least one root and a subset of the finite Galois field as candidates by executing a Gaussian Elimination process using selective exponentiation as a linear operator over GF(2) and determining the remaining roots by iteratively substituting the candidates in the system of equations until said equations are satisfied; and (d) determining error values from the syndromes at locations in the received word specified by the extracted roots of the counterpart error locator polynomial and logically combining said determined error values with the counterpart received word in error to form a corrected word.