Difference systems of sets (DSSs) introduced by Levenstein are combinatorial structures used to construct comma-free codes for synchronization. In this letter, two classes of optimal DSSs are presented. One class is obtained based on q-ary ideal sequences with d-form property and difference-balanced property. The other class of optimal and perfect DSSs is derived from perfect ternary sequences given by Ipatov in 1995. Compared with known constructions (Zhou, Tang, Optimal and perfect difference systems of sets from q-ary sequences with difference-balanced property, Des. Codes Cryptography, 57(2), 215-223, 2010), the proposed DSSs lead to comma-free codes with nonzero code rate.

In this paper, for any given prime power q, using Helleseth-Gong sequences with ideal auto-correlation property, we propose a class of perfect sequences of length (qm-1)/(q-1). As an application, a subclass of constructed perfect sequences is used to design optimal and perfect difference systems of sets.

In this paper, we present two classes of zero difference balanced (ZDB) functions, which are derived by difference balanced functions, and a class of perfect ternary sequences respectively. The proposed functions have parameters not covered in the literature, and can be used to design optimal constant composition codes, and perfect difference systems of sets.

An asymmetric zero correlation zone (A-ZCZ) sequence set is a type of ZCZ sequence set and consists of multiple sequence subsets. It is the most important property that is the cross-correlation function between arbitrary sequences belonging to different sequence subsets has quite a large zero-cross-correlation zone (ZCCZ). Our proposed A-ZCZ sequence sets can be constructed based on interleaved technique and orthogonality-preserving transformation by any perfect sequence of length P=Nq(2k+1) and Hadamard matrices of order T≥2, where N≥1, q≥1 and k≥1. If q=1, the novel sequence set is optimal ZCZ sequence set, which has parameters (TP,TN,2k+1) for all positive integers P=N(2k+1). The proposed A-ZCZ sequence sets have much larger ZCCZ, which are expected to be useful for designing spreading sequences for QS-CDMA systems.

This letter presents a framework, including two constructions, for yielding several types of sequences with optimal autocorrelation properties. Only by simply choosing proper coefficients in constructions and optimal known sequences, two constructions transform the chosen sequences into optimally required ones with two or four times periods as long as the original sequences', respectively. These two constructions result in binary and quaternary sequences with optimal autocorrelation values (OAVs), perfect QPSK+ sequences, and multilevel perfect sequences, depending on choices of the known sequences employed. In addition, Construction 2 is a generalization of Construction B in [5] so that the number of distinct sequences from the former is larger than the one from the latter.

This paper investigates construction methods of perfect 16-QAM sequences and arrays, since such sequences and arrays play quite an important role in synchronization of communication systems making use of 16-QAM signals. The method used for obtaining the results is to establish a relationship between the known perfect quaternary sequences/arrays and the required ones so that the former is transformed into the latter. Consequently, the sufficient conditions for implementing the required transformations are derived, and several examples are given. Our methods can provide perfect 16-QAM sequences with lengths 2, 4, 8, and 16, which are given in Table A·1 and infinite families of perfect 16-QAM arrays, whose existing sizes up to dimension 5 and volume 2304 are listed in Tables A·2 and A·3.

In our previous work, we have proposed a method for constructing ZCZ sequence sets. The method proposed by the previous work is based on perfect sequences and unitary matrices. This method can generate ZCZ sequence sets which possess a good feature concerning the length of zero-correlation zones. In this letter, we propose a new method for constructing ZCZ sequence sets by improving the previous method. The proposed method can generate new ZCZ sequence sets which can not be obtained from the previous method. These ZCZ sequence sets also possess the good feature concerning the length of zero-correlation zones.