Cyclic inequivalence of cascaded GMW-sequences

Cascaded GMW sequences have two-level autocorrelation functions, which have important applications in communications and cryptology. In this paper, we consider the cascaded GMW sequences corresponding to a fixed finite chain of finite fields, and determine whether the different cascaded GMW sequences are cyclically inequivalent. By introducing the so-called restricted integer systems (RISs), it is proved that all the cascaded GMW sequences can be determined by means of the RISs, and the sequences determined by different RISs are different. Moreover, different cascaded GMW sequences are cyclically inequivalent.