Binary sequence pairs with optimal periodic correlation have important applications in many fields of communication systems. In this letter, four new families of binary sequence pairs are presented based on the generalized cyclotomy over Z5q, where q ≠ 5 is an odd prime. All these binary sequence pairs have optimal three-level correlation values {-1, 3}.

Based on the number of cyclotomy of order eight, a class of balanced almost 8-QAM sequences with odd prime periods is presented. The resultant sequences have low two-level nontrivial autocorrelation values, and their distribution is determined. Furthermore, the smallest possible absolute sidelobes (SPASs) of autocorrelation functions of balanced almost 8-QAM sequences are derived. Compared with the obtained SPASs, some of the proposed sequences is optimal or suboptimal.

Pseudo-random sequences with good statistical property, such as low autocorrelation, high linear complexity and 2-adic complexity, have been widely applied to designing reliable stream ciphers. In this paper, we explicitly determine the 2-adic complexities of two classes of generalized cyclotomic binary sequences with order 4. Our results show that the 2-adic complexities of both of the sequences attain the maximum. Thus, they are large enough to resist the attack of the rational approximation algorithm for feedback with carry shift registers. We also present some examples to illustrate the validity of the results by Magma programs.

Two new families of balanced almost binary sequences with a single zero element of period L=2q are presented in this letter, where q=4d+1 is an odd prime number. These sequences have optimal autocorrelation value or optimal autocorrelation magnitude. Our constructions are based on cyclotomy and Chinese Remainder Theorem.

As an optimal combinatorial object, cyclic perfect Mendelsohn difference family (CPMDF) was introduced by Fuji-Hara and Miao to construct optimal optical orthogonal codes. In this paper, we propose a direct construction of disjoint CPMDFs from the Zeng-Cai-Tang-Yang cyclotomy. Compared with a recent work of Fan, Cai, and Tang, our construction doesn't need to depend on a cyclic difference matrix. Furthermore, strictly optimal frequency-hopping sequences (FHSs) are a kind of optimal FHSs which has optimal Hamming auto-correlation for any correlation window. As an application of our disjoint CPMDFs, we present more flexible combinatorial constructions of strictly optimal FHSs, which interpret the previous construction proposed by Cai, Zhou, Yang, and Tang.

In this letter, two new families of quaternary sequences with low four-level or five-level autocorrelation are constructed based on generalized cyclotomy over Z2p. These quaternary sequences are balanced and the maximal absolute value of the out-of-phase autocorrelation is 4.

In this paper, a new generalized cyclotomy over Zpq is presented based on cyclotomy and Chinese remainder theorem, where p and q are different odd primes. Several new construction methods for binary sequence pairs of period pq with ideal two-level correlation are given by utilizing these generalized cyclotomic classes. All the binary sequence pairs from our constructions have both ideal out-of-phase correlation values -1 and optimum balance property.

New classes of zero-difference balanced (ZDB) functions derived from Fermat quotients are proposed in this letter. Based on the new ZDB functions, some applications, such as the construction of optimal frequency hopping sequences set and perfect difference systems of sets, are introduced.

Jacobi sequences have good cryptography properties. Li et al. [X. Li et al., Linear Complexity of a New Generalized Cyclotomic Sequence of Order Two of Length pq*, IEICE Trans. Fundamentals, vol.E96-A, no.5, pp.1001-1005, 2013] defined a new modified Jacobi sequence of order two and got its linear complexity. In this corresponding, we determine the linear complexity and minimal polynomials of the new modified Jacobi sequence of order d. Our results show that the sequence is good from the viewpoint of linear complexity.

In this letter, by using Whiteman's generalized cyclotomy of order 2 over Zpq, where p, q are twin primes, we construct new perfect Gaussian integer sequences of period pq.

In this letter, we generalize the binary sequence introduced by Li et al. in [S. Q. Li et al., On the randomness generalized cyclotomic sequences of order two and length pq, IEICE Trans. Fund, vol. E90-A, no.9, pp.2037-2041, 2007] to sequence over arbitrary prime fields. Furthermore, the auto-correlation distribution and linear complexity of the proposed sequence are presented.

In this paper, we compare two generalized cyclotomic binary sequences with length 2p2 in terms of the linear complexity. One classical sequence is defined using the method introduced by Ding and Helleseth, while the other modified sequence is defined in a slightly different manner. We show that the modified sequence has linear complexity of 2p2, which is higher than that of the classical one.

In this letter we introduce new generalized cyclotomic sequences of order two and length pq firstly, then we determine the linear complexity and autocorrelation values of these sequences. Our results show that these sequences are rather good from the linear complexity viewpoint.

This paper contributes to a new generalized cyclotomic sequences of order two with respect to p1e1p2e2… ptet. The emphasis is on the linear complexity and autocorrelation of new prime-square sequences and two-prime sequences, two special cases of these generalized cyclotomic sequences. Our method is based on their characteristic polynomials. Results show that these sequences possess good linear complexity. Under certain conditions, the autocorrelation functions of new prime-square sequences and two-prime sequences may be three-valued.