A new approach to the Berlekamp-Massey-Sakata Algorithm. Improving Locator Decoding

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 algor...

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Bibliographic Details
Published in:arXiv.org 2024-01
Main Authors: Bernal, José Joaquín, Juan Jacobo Simón
Format: Article
Language:English
Subjects:
Algorithms
Decoding
Iterative methods
Polynomials
Rings (mathematics)
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2401.10527