A new approach to the Berlekamp-Massey-Sakata Algorithm. Improving Locator Decoding
Information Theory
2024-01-22 v1 math.IT
Abstract
We study the problem of the computation of Groebner basis for the ideal of linear recurring relations of a doubly periodic array. We find a set of indexes such that, along with some conditions, guarantees that the set of polynomials obtained at the last iteration in the Berlekamp-Massey-Sakata algorithm is exactly a Groebner basis for the mentioned ideal. Then, we apply these results to improve locator decoding in abelian codes.
Keywords
Cite
@article{arxiv.2401.10527,
title = {A new approach to the Berlekamp-Massey-Sakata Algorithm. Improving Locator Decoding},
author = {José Joaquín Bernal and Juan Jacobo Simón},
journal= {arXiv preprint arXiv:2401.10527},
year = {2024}
}
Comments
21 pages