Multiple-sequence BM algorithm can be replaced by a succession of single-sequence BM algorithm

We present a simple modification of the Berlekamp-Massey (BM) algorithm by which one can solve the problem solved by the ´multiple-sequence BM algorithm´ [Feng and Tzeng, IEEE IT Trans. 1989, 1991]. The original BM algorithm which we call ´single-sequence BM algorithm´ finds a simplest linear feedback shift register (LFSR) capable of generating a given (single) sequence while the multiple-sequence BM algorithm finds a simplest LFSR capable of generating each of given (multiple) sequences. We have only to repeat our algorithm with reinitialization. The computational complexity is the same as the multiple-sequence BM algorithm. It allows that given sequences have different lengths