Decoding Binary Cyclic Codes with Irreducible Generator Polynomials up to Actual Minimum Distance

This letter presents two modified algorithms to decode up to actual minimum distance for binary cyclic codes with irreducible generator polynomials. The key ideas behind these decoding algorithms are the utilization of the extended Euclid´s algorithm for univariate polynomials to evaluate the unknown syndromes and the coefficients of general error locator polynomial, which has not been developed before. The advantage of these algorithms is particularly suitable for software and hardware implementations.