Decoding a Class of Affine Variety Codes with Fast DFT
Abstract
An efficient procedure for error-value calculations based on fast discrete Fourier transforms (DFT) in conjunction with Berlekamp-Massey-Sakata algorithm for a class of affine variety codes is proposed. Our procedure is achieved by multidimensional DFT and linear recurrence relations from Grobner basis and is applied to erasure-and-error decoding and systematic encoding. The computational complexity of error-value calculations in our algorithm improves that in solving systems of linear equations from error correcting pairs in many cases. A motivating example of our algorithm in case of a Reed-Solomon code and a numerical example of our algorithm in case of a Hermitian code are also described.
Cite
@article{arxiv.1210.0083,
title = {Decoding a Class of Affine Variety Codes with Fast DFT},
author = {Hajime Matsui},
journal= {arXiv preprint arXiv:1210.0083},
year = {2012}
}
Comments
5 pages, 1 figure, to be presented at 2012 International Symposium on Information Theory and its Applications (ISITA2012)