General Shift-Register Sequences of Arbitrary Cycle Length
Alvay Ray Smith · IEEE Transactions on Computers · 1971
An r-ary shift-register sequence is desired that has arbitrary cycle length L≤rkfor arbitrary r and k, where k is the number of stages (degree) of the shift register. The existence of such sequences is established for "almost all" cycle lengths L. Furthermore, existence of such sequences which are "zero free" for almost all cycle lengths L is proved.