English

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

R2 v1 2026-06-28T14:21:16.345Z