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

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ABMS_Bernal_Simon_Arxiv.pdf(366.06 KB)
Date
2021
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Authors
Bernal Buitrago, José Joaquín ; Simón Pinero, Juan Jacobo
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Publisher
IEEE
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Matemáticas
DOI
https://doi.org/10.1109/TIT.2020.3027751
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info:eu-repo/semantics/article
Description
©2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ This document is the Accepted, version of a Published Work that appeared in final form in IEEE Transactions on Information Theory. To access the final edited and published work see https://doi.org/10.1109/TIT.2020.3027751
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.
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Abelian codes , Berlekamp-Massey-Sakata algorithm , Groebner basis , Linear recurring relations
Citation
IEEE Trans. Inform. Theory. Vol. 67(1), 2021, 268-281.
URI
http://hdl.handle.net/10201/137544
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