Inspired by an idea due to Levenshtein, we apply the low correlation zone constraint in the analysis of the weighted mean square aperiodic correlation. Then we derive a lower bound on the measure for quasi-complementary sequence sets with low correlation zone (LCZ-QCSS). We discuss the conditions of tightness for the proposed bound. It turns out that the proposed bound is tighter than Liu-Guan-Ng-Chen bound for LCZ-QCSS. We also derive a lower bound for QCSS, which improves the Liu-Guan-Mow bound in general.

In this correspondence, a generic method of constructing optimal p2-ary low correlation zone sequence sets is proposed. Firstly p2-ary column sequence sets are constructed, then p2-ary LCZ sequence sets with parameters (pn-1, pm-1, (pn-1)/(pm-1),1) are constructed by using column sequences and interleaving technique. The resultant p2-ary LCZ sequence sets are optimal with respect to the Tang-Fan-Matsufuji bound.

In this paper, we constructed a class of low correlation zone sequence sets derived from the interleaved technique and DFT matrices. When p is a prime such that p > 3, p-ary LCZ sequence sets with parameters LCZ(pn-1,pm-1,(pn-1)/(pm-1),1) are constructed based on a DFT matrix with order pp, which is optimal with respect to the Tang-Fan-Matsufuji bound. When p is a prime such that p ≥ 2, pk-ary LCZ sequence sets with parameters LCZ(pn-1,pk-1,(pn-1)/(pk-1),1) are constructed based on a DFT matrix with order pkpk, which is also optimal. These sequence sets are useful in certain quasi-synchronous code-division mutiple access (QS-CDMA) communication systems.

In this letter, we present a general construction of sequence sets with low correlation zone, which is based on finite fields and the balance property of some functions. The construction is more flexible as far as the partition of parameters is concerned. A simple example is also given to interpret the construction.

In this correspondence, a new method to extend the number of quaternary low correlation zone (LCZ) sequence sets is presented. Based on the inverse Gray mapping and a binary sequence with ideal two-level auto-correlation function, numbers of quaternary LCZ sequence sets can be generated by choosing different parameters. There is at most one sequence cyclically equivalent in different LCZ sequence sets. The parameters of LCZ sequence sets are flexible.

In this letter, we propose a new construction of quaternary low correlation zone (LCZ) sequence set using binary LCZ sequence sets and an inverse Gray mapping. The new construction method provides optimal quaternary LCZ sequence sets even if the employed binary LCZ sequence set is suboptimal. The optimality is improved at the price of alphabet extension.

In this paper, we propose four new general constructions of LCZ/ZCZ sequence sets based on interleaving technique and affine transformations. A larger family of LCZ/ZCZ sequence sets with longer period are generated by these constructions, which are more flexible among the selection of the alphabet size, the period of the sequences and the length of LCZ/ZCZ, compared with those generated by the known constructions. Especially, two families of the newly constructed sequences can achieve or almost achieve the theoretic bound.

We propose an extension method of quaternary low correlation zone (LCZ) sequence set with odd period. From a quaternary LCZ sequence set with parameters (N, M, L, 1), the proposed method constructs a new quaternary LCZ sequence set with parameters (2N, 2M, L, 2), where N is odd. If the employed LCZ sequence set in the construction is optimal, the extended LCZ sequence set becomes also optimal where N = kL, L > 4, and k>2.

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.

In this paper, given an integer e and n such that e|n, and a prime p, we propose a method of constructing optimal p2-ary low correlation zone (LCZ) sequence set with parameters (pn-1, pe-1, (pn -1)/(pe -1), 1) from a p-ary sequence of the same length with ideal autocorrelation. The resulting p2-ary LCZ sequence set can be viewed as the generalization of the optimal quaternary LCZ sequence set by Kim, Jang, No, and Chung in respect of the alphabet size. This generalization becomes possible due to a completely new proof comprising any prime p. Under this proof, the quaternary case can be considered as a specific example for p = 2.