Multi-continued fraction algorithm and generalized B–M algorithm over Fq

An iterative algorithm in solving the linear synthesis problem on multi-sequences over finite fields is derived from the multi-strict continued fraction algorithm (m-SCFA in short). It is interesting that the derived iterative algorithm is the same as the generalized Berlekamp–Massey algorithm (GBMA in short), though the computations in the m-SCFA and the GBMA are completely different. As a consequence, the minimal polynomials and the discrepancy sequence obtained by acting GBMA on a multi-sequence are expressed explicitly by data associated to the multi-strict continued fraction expansion of .