Abstract
We derive the Wu list-decoding algorithm for generalized Reed–Solomon (GRS) codes by using Gröbner bases over modules and the Euclidean algorithm as the initial algorithm instead of the Berlekamp–Massey algorithm. 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, 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.
Original language | English |
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Journal | I E E E Transactions on Information Theory |
Volume | 59 |
Issue number | 6 |
Pages (from-to) | 3269-3281 |
ISSN | 0018-9448 |
DOIs | |
Publication status | Published - 2013 |
Bibliographical note
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