A generalization of the Massey-Ding algorithm (Q1389143)

In [Finite linear recurring sequences and homogeneous ideals, same journal 7, 377-390 (1996; Zbl 0870.11009)], the authors described the complete solution of the synthesis problem by computing a Gröbner basis of the annihilator ideal for a set of finite linear recurring sequences. In the present paper the authors use their ideal theoretic approach in order to generalize the Massey-Ding algorithm. The latter one computes a linear recurrence relation of minimal order for several finite sequences of equal length, while the generalization allows the computation of a minimal Gröbner basis of the annihilator ideal of several finite sequences of generally different lengths.