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A Recursive Relation Between The Adjacency Graph of Some LFSRs and Its Applications

In this paper, a general way to determine the adjacency graph of linear feedback shift registers (LFSRs) with characteristic polynomial (1 + x)c(x) from the adjacency graph of LFSR with characteristic polynomial c(x) is discussed, where c(x) can be any polynomial. As an application, the adjacency graph of LFSRs with characteristic polynomial (1+ x)p(x) are determined, where p(x) is a primitive polynomial. Besides, some properties about the cycles in LFSRs are presented. The adjacency graph of LFSRs with characteristic polynomial (1 + x)p(x) are also discussed.