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A lattice basis reduction multisequence synthesis (LBRMS) algorithm was presented with a new, intuitive and vector-form model. In this paper, a refined version of the LBRMS algorithm is deduced, from which Massey's conjectured algorithm can be derived. Moreover, if we modify the lattice basis reduction algorithm used in the LBRMS algorithm, a new synthesis algorithm is deduced, which is equivalent to the generalization of the Berlekamp-Massey algorithm proposed by Feng and Tzeng (1989). Therefore, the LBRMS algorithm provides a unified approach to the multisequence shift-register synthesis problem.