List decoding for binary Goppa codes

Authors:
Daniel J. Bernstein
Affiliations:
Department of Computer Science, University of Illinois at Chicago, Chicago, IL
Venue:
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
Year:
2011

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Abstract

This paper presents a Patterson-style list-decoding algorithm for classical irreducible binary Goppa codes. The algorithm corrects, in polynomial time, approximately n-√n(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 t2/2n extra errors.