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 xed nite chain of nite elds, and study the problem of how to determine all these diierent cascaded GMW sequences without repetition, and the problem of whether the diierent 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 diierent RISs are diierent. Moreover, diierent cascaded GMW sequences are cyclically inequivalent. Abstract 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 xed nite chain of nite elds, and study the problem of how to determine all these diierent cascaded GMW sequences without repetition, and the problem of whether the diierent 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 diierent RISs are diierent. Moreover, diierent cascaded GMW sequences are cyclically inequivalent.