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arXiv · 2401.10527

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

José Joaquín Bernal·Juan Jacobo Simón
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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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José Joaquín Bernal, Juan Jacobo Simón. 2024-01-19. A new approach to the Berlekamp-Massey-Sakata Algorithm. Improving Locator Decoding. https://doi.org/10.1109/tit.2020.3027751

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