In this paper we propose a linear shift register synthesis algorithm for a multisequence of varying length by modifying the lattice basis reduction multisequence synthesis (Wang-Zhu-Pei for short) algorithm [9]. After a few simple modifications to it we can obtain the Schmidt-Sidorenko algorithm in [5]. In addition, we give the necessary and sufficient condition for the uniqueness of the minimal-length linear shift-register for generating a multisequence of varying length.
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