Encoding via Gr\"obner bases and discrete Fourier transforms for several types of algebraic codes
Information Theory
2007-07-13 v2 math.IT
Abstract
We propose a novel encoding scheme for algebraic codes such as codes on algebraic curves, multidimensional cyclic codes, and hyperbolic cascaded Reed-Solomon codes and present numerical examples. We employ the recurrence from the Gr\"obner basis of the locator ideal for a set of rational points and the two-dimensional inverse discrete Fourier transform. We generalize the functioning of the generator polynomial for Reed-Solomon codes and develop systematic encoding for various algebraic codes.
Cite
@article{arxiv.cs/0703104,
title = {Encoding via Gr\"obner bases and discrete Fourier transforms for several types of algebraic codes},
author = {Hajime Matsui and Seiichi Mita},
journal= {arXiv preprint arXiv:cs/0703104},
year = {2007}
}
Comments
5 pages, 4 figures, To be presented at IEEE International Symposium on Information Theory 2007