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.

翻译：我们研究计算双周期阵列线性递归关系理想格罗布纳基的问题。我们找到一组索引，在满足特定条件的前提下，可确保Berlekamp-Massey-Sakata算法最后一次迭代得到的多项式集合恰好是该理想的格罗布纳基。进而，我们将这些结果应用于改进阿贝尔码的定位子解码。