On PGZ decoding of alternant codes

In this paper, we first review the classical Petterson–Gorenstein–Zierler decoding algorithm for the class of alternant codes, which includes Reed–Solomon, Bose–Chaudhuri–Hocquenghem and classical Goppa codes. Afterwards, we present an improvement of the method to find the number of errors and the error-locator polynomial. Finally, we illustrate the procedure with several examples. In two appendices, we sketch the main features of the computer algebra system designed and developed to support the computations.