ABSTRACT

An r-ary shift-register sequence is desired that has arbitrary cycle length L=r<sup>k</sup>for 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.

INDEX TERMS

Coding theory, maximum-length cycle, shift-register sequence, zero free.

CITATION

A. Smith, "General Shift-Register Sequences of Arbitrary Cycle Length," in

*IEEE Transactions on Computers*, vol. 20, no. , pp. 456-459, 1971.

doi:10.1109/T-C.1971.223265

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