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

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.

preprint2013arXivOpen access
Peter BeelenTom HøholdtJohan S. R. NielsenYingquan Wu
math.ITInformation Theory
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Peter BeelenTom HøholdtJohan S. R. NielsenYingquan Wu

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