Cyclic inequivalence of cascaded GMW-sequences

AbstractCascaded 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

A Family of Binary Sequences with Optimal Correlation Property and Large Linear Span

A family of binary sequences is presented and proved to have optimal correlation property and large linear span. It includes the small set of Kasami sequences, No sequence set and TN sequence set as special cases. An explicit lower bound expression on the linear span of sequences in the family is given. With suitable choices of parameters, it is proved that the family has exponentially larger linear spans than both No sequences and TN sequences. A class of ideal autocorrelation sequences is also constructed and proved to have large linear span.Comment: 21 page

A Hardware Oriented Method to Generate and Evaluate Nonlinear Interleaved Sequences with Desired properties

It is well known that the combinatorial structure, algebraic structure and D-transform based method render the nonlinear sequences with good autocorrelation function (ACF) and great linear complexity (LC). However, “all sequences” are not equal even if they are “born” by the same method! In this paper the big inequalities regarding LC of these sequences are shown based on a hardware oriented method (D-transform). In order to get the right sequences some more extensive simulations and trade off are needed. That is why this paper is represented here with above Title. Keywords: cryptography, mobile communications, security, watermarking, D-transfor