A New Approach to the Berlekamp-Massey-Sakata Algorithm: Improving Locator Decoding
José Joaquín Bernal, Juan Jacobo Simón · IEEE Transactions on Information Theory · 2020
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.