Paper 2014/686

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

Ming Li and Dongdai Lin

Abstract

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)^4p(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)^mp(x) are also discussed.

Note: Some applications are added. Some proofs are simplified.