Method for locating four errors in a reed-solomon or bch code

摘要

A system determines the error locations of four errors in GF(22m) by transforming a degree-four error locator polynomial ultimately into two quadratic equations, finding the solutions of these equations, and from these solutions determining the roots of an error locator polynomial. The system first manipulates the error locator polynomial, which is of the form: sigma (x)= sigma 4x4+ sigma 3x3 sigma 2x2+ sigma 1x+ sigma 0 [1]into the form: theta (y)=y4+ theta 2y2+ theta 1y+ theta 0 [2]where the theta i's are combinations of the coefficients of the terms of the error locator polynomial. The system has thus produced an equation in which the coefficient of the y3 term is 0. The system then factors theta (y), to produce theta (y)=(y2+t*y+u)*(y2+v*y+w), [3]where "*" represents multiplication. It then determines the values of t, u, v and w by equating the coefficients of the two expressions for theta (y) and solving first for the variable t, which is equal to v, and then for the variables w and u. Once the values of the variables are determined, the system solves two quadratic equations, one for each of the factors of equation 3. Based on these solutions, the system determines the four error locations associated with the degree-four error locator polynomial.