A lattice-based linear shift register synthesis for multisequences of varying length

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 (L.-P. Wang et al., 2004). After a few simple modifications to it we can obtain the Schmidt-Sidorenko algorithm in (G. Schmidt and V.R. Sidorenko, 2006). 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.