On Rational-Interpolation Based List-Decoding and List-Decoding Binary Goppa Codes
Abstract
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) 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.
Keywords
Cite
@article{arxiv.1211.0122,
title = {On Rational-Interpolation Based List-Decoding and List-Decoding Binary Goppa Codes},
author = {Peter Beelen and Tom Høholdt and Johan S. R. Nielsen and Yingquan Wu},
journal= {arXiv preprint arXiv:1211.0122},
year = {2013}
}
Comments
To appear in IEEE Transactions of Information Theory