Investigating some special sequence lengths generated in an external exclusive-NOR type LFSR

The study of the length of Pseudo-Random Binary Sequences (PRBS) generated by Linear Feedback Shift Registers (LFSRs) play an important role in design approaches of Built-In Self Test (BIST), cryptosystems, and other applications. It is not taken to be granted that primitive characteristic polynomials always generate maximal length PRBSs. This paper investigates many such conditions where LFSR structures restrict the PRBS generation to a certain fixed length. This study will surely help the designers of the BIST equipments and cryptosystems. The outcome of this paper is presented in the forms of theorems, simulations, and analyses which strongly supports the findings.