Journal article · Preprint article
On Rational Interpolation-Based List-Decoding and List-Decoding Binary Goppa Codes
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.
Language: | English |
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Publisher: | IEEE |
Year: | 2013 |
Pages: | 3269-3281 |
ISSN: | 15579654 and 00189448 |
Types: | Journal article and Preprint article |
DOI: | 10.1109/TIT.2013.2243800 |
ORCIDs: | Beelen, Peter and Nielsen, Johan Sebastian Rosenkilde |