On PGZ decoding of alternant codes
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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.
KeywordsAlternant codes RS codes BCH codes Classical Goppa codes Computer algebra systems
Mathematics Subject Classification11T71 94B05 94B35 94B15
The authors are grateful to the anonymous referees for having pointed out a number of misprints and suggested some style changes.
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