We derive the Wu list-decoding algorithm for Generalised Reed-Solomon (GRS)codes by using Gr\"obner bases over modules and the Euclidean algorithm (EA) asthe initial algorithm instead of the Berlekamp-Massey algorithm (BMA). Wepresent a novel method for constructing the interpolation polynomial fast. Wegive a new application of the Wu list decoder by decoding irreducible binaryGoppa codes up to the binary Johnson radius. Finally, we point out a connectionbetween the governing equations of the Wu algorithm and the Guruswami-Sudanalgorithm (GSA), immediately leading to equality in the decoding range and aduality in the choice of parameters needed for decoding, both in the case ofGRS codes and in the case of Goppa codes.
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