In this letter we propose a new Whiteman generalized cyclotomic sequence of order 4. Meanwhile, we determine its linear complexity and minimal polynomial. The results show that this sequence possesses both high linear complexity and optimal balance on 1 s and 0 s, which may be attractive for cryptographic applications.

In this letter, we first introduce a new generalized cyclotomic sequence of order two of length pq, then we calculate its linear complexity and minimal polynomial. Our results show that this sequence possesses both high linear complexity and optimal balance on 1s and 0s, which may be attractive for use in stream cipher cryptosystems.

This paper contributes to k-error linear complexity of some generalized cyclotomic binary sequences of length 2p(m) and p(m) constructed in recent years. By defining related reference sequences, we find that these sequences possess very low k-error linear complexity for some certain values of the parameter k even though they have high linear complexity. Moreover, we point out that (p - 1)-tuple distributions of all these sequences are not span. Thus they should be selected carefully for use in stream cipher systems.

The aim of this paper is to study a class of strong Dubreil-Jacotin semigroups, so-called split integral Dubreil-Jacotin semigroups. We establish the structure of split integral Dubreil-Jacotin semigroups in terms of the cartesian ordered semidirect product of an ordered monoid and an ordered group. Also, the lexicographic ordered semidirect product is considered. These results extend main results in [1].