Abstract
Shift register generator (SRG) is an autonomous system consisting of shift registers and exclusive-OR gates. In this chapter, we investigate the behaviors of SRGs in view of the sequence space theory developed in the previous chapter. For a given SRG, we first consider how to determine the sequence space generated by SRG sequences with a fixed initial state vector (SRG space), and then consider how to find the largest-dimensional sequence space that can be obtained by varying the initial state vectors (SRG maximal space). Conversely, for a given sequence space we consider how to find the minimum-sized SRGs that can generate the sequence space (basic SRG). Finally, we examine the two typical SRGs, namely the simple SRG and the modular SRG, in view of the concept of basic SRGs.
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