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arXiv · 1211.0122

On Rational-Interpolation Based List-Decoding and List-Decoding Binary Goppa Codes

Peter Beelen·Tom Høholdt·Johan S. R. Nielsen·Yingquan Wu
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Abstract

We derive the Wu list-decoding algorithm for Generalised Reed-Solomon (GRS) codes by using Gröbner bases over modules and the Euclidean algorithm (EA) as the initial algorithm instead of the Berlekamp-Massey algorithm (BMA). We present a novel method for constructing the interpolation polynomial fast. We give a new application of the Wu list decoder by decoding irreducible binary Goppa codes up to the binary Johnson radius. Finally, we point out a connection between the governing equations of the Wu algorithm and the Guruswami-Sudan algorithm (GSA), immediately leading to equality in the decoding range and a duality in the choice of parameters needed for decoding, both in the case of GRS codes and in the case of Goppa codes.

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Peter Beelen, Tom Høholdt, Johan S. R. Nielsen, Yingquan Wu. 2013-02-25. On Rational-Interpolation Based List-Decoding and List-Decoding Binary Goppa Codes. https://doi.org/10.1109/tit.2013.2243800

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