In frequency-hopping (FH) multiple access systems, frequency-hopping sequences (FHSs) with optimal Hamming correlation properties are needed. Based on the d-form functions with ideal autocorrelation properties, a new set of FHSs is constructed. The new FHS set is optimal with respect to the Peng-Fan bounds and each FHS in the set is optimal with respect to the Lempel-Greenberger bound.

In this paper, based on interleaved technique, we present a new method of constructing zero correlation zone (ZCZ) sequence sets. For any perfect sequence of length m(2k+1) with m > 2, k ≥ 0 and an arbitrary Hadamard matrix of order T > 2, the proposed construction can generate new optimal ZCZ sequence sets in which all the sequences are cyclically distinct.

In this paper, for odd n and any k with gcd(n,k) = 1, new binary sequence families Sk of period 2n-1 are constructed. These families have maximum correlation , family size 22n+2n+1 and maximum linear span . The correlation distribution of Sk is completely determined as well. Compared with the modified Gold codes with the same family size, the proposed families have the same period and correlation properties, but larger linear span. As good candidates with low correlation and large family size, the new families contain the Gold sequences and the Gold-like sequences. Furthermore, Sk includes a subfamily which has the same period, correlation distribution, family size and linear span as the family So(2) recently constructed by Yu and Gong. In particular, when k=1, is exactly So(2).

Recently there has been a surge of interest in construction of low correlation zone sequences. The purpose of this paper is to survey the known results in the area and to present an interleaved construction of binary low correlation zone sequences. The interleaved construction unifies many constructions currently available in the literature. These sequences are useful in quasi-synchronous code-division multiple access (QS-CDMA) communication systems.

Aperiodic quadriphase Z-complementary sequences, which include the conventional complementary sequences as special cases, are introduced. It is shown that, the aperiodic quadriphase Z-complementary pairs are normally better than binary ones of the same length, in terms of the number of Z-complementary pairs, and the maximum zero correlation zone. New notions of elementary transformations on quadriphase sequences and elementary operations on sets of quadriphase Z-complementary sequences are presented. In particular, new methods for analyzing the relations among the formulas relative to sets of quadriphase Z-complementary sequences and for describing the sets are proposed. The existence problem of Z-complementary pairs of quadriphase sequences with zero correlation zone equal to 2, 3, and 4 is investigated. Constructions of sets of quadriphase Z-complementary sequences and their mates are given.

Let n,k,e,m be positive integers such that n≥ 3, 1 ≤ k ≤ n-1, gcd(n,k)=e, and m= is odd. In this paper, for an odd prime p, we derive a lower bound for the minimal distance of a large class of p-ary cyclic codes Cl with nonzeros α-1, α-(pk+1), α-(p3k+1), …, α-(p(2l-1)k+1), where 1 ≤ l ≤ and α is a primitive element of the finite field Fpn. Employing these codes, p-ary sequence families with a flexible tradeoff between low correlation and large size are constructed.

In this letter, new families of binary low correlation zone (LCZ) sequences based on the interleaving technique and quadratic form sequences are constructed, which include the binary LCZ sequence set derived from Gordon-Mills-Welch (GMW) sequences. The constructed sequences have the property that, in a specified zone, the out-of-phase autocorrelation and cross-correlation values are all equal to -1. Due to this property, such sequences are suitable for quasi-synchronous code-division multiple access (QS-CDMA) systems.

For an odd prime p, two new families of p-ary sequences of period pn-1 are constructed for odd n = 2l+1=(2m+1)e and even n = 2l = 2me, respectively. It is shown that, for a given integer ρ with 1 ≤ ρ ≤ m, the proposed sequence families both have maximum correlation magnitude , family size (pn-1)p(ρ-1)n+1, and maximum linear span .