For any integer N > 1, we construct feedback with carry shift registers over Z/(N) (N -FCSRs). The case when N is a prime, was investigated by Klapper and Goresky [1, 2]. We present the basic properties of N -FCSRs. We solve the register synthesis problem: given a small number of symbols of a sequence over Z/(N) synthesize the smallest N -FCSR that outputs the sequence.

Let a be an l-sequence generated by a feedback-with-carry shift register with connection integer q = pe, where p is an odd prime and e 1. Goresky and Klapper conjectured that when pe = 2 f5; 9; 11; 13g, all decimations of a are cyclically distinct. When e = 1 and p > 13, they showed that the set of distinct decimations is large and, in some cases, all deciamtions are distinct. In this article, ...