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This paper presents a Patterson-style list-decoding algorithm for classical irreducible binary Goppa codes. The algorithm corrects, in polynomial time, approximately $n-\sqrtn(n-2t-2)$ errors in a length-n classical irreducible degree-t binary Goppa code. Compared to the best previous polynomial-time list-decoding algorithms for the same codes, the new algorithm corrects approximately $t^2\!/2n$ extra errors.
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