A new approach to the Berlekamp-Massey-Sakata Algorithm. Improving Locator Decoding
arXiv:2401.10527 · doi: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.
21 pages