In this paper we obtain a new method to compute the correlation values of two arbitrary sequences defined by a mapping from F4n to F4. We apply this method to demonstrate that the usual nonbinary maximal length sequences have almost ideal correlation under the canonical complex correlation definition and investigate some decimations giving good cross correlation. The techniques we develop are of independent interest for future investigation of sequence design and related problems, including Boolean functions.

A set consisting of K subsets of Msequences of length L is called a complementary sequence set expressed by A(L, K, M), if the sum of the out-of-phase aperiodic autocorrelation functions of the sequences within a subset and the sum of the cross-correlation functions between the corresponding sequences in any two subsets are zero at any phase shift. Suehiro et al. first proposed complementary set A(Nn, N, N) where N and n are positive integers greater than or equal to 2. Recently, several complementary sets related to Suehiro's construction, such as N being a power of a prime number, have been proposed. However, there is no discussion about their inclusion relation and properties of sequences. This paper rigorously formulates and investigates the (generalized) logic functions of the complementary sets by Suehiro et al. in order to understand its construction method and the properties of sequences. As a result, it is shown that there exists a case where the logic function is bent when n is even. This means that each series can be guaranteed to have pseudo-random properties to some extent. In other words, it means that the complementary set can be successfully applied to communication on fluctuating channels. The logic functions also allow simplification of sequence generators and their matched filters.

AlphaSeq is a new paradigm to design sequencess with desired properties based on deep reinforcement learning (DRL). In this work, we propose a new metric function and a new reward function, to design an improved version of AlphaSeq. We show analytically and also through numerical simulations that the proposed algorithm can discover sequence sets with preferable properties faster than that of the previous algorithm.

Z-complementary pairs (ZCPs) were proposed by Fan et al. to make up for the scarcity of Golay complementary pairs. A ZCP of odd length N is called Z-optimal if its zero correlation zone width can achieve the maximum value (N + 1)/2. In this letter, inserting three elements to a GCP of length L, or deleting a point of a GCP of length L, we propose two constructions of Z-optimal ZCPs with length L + 3 and L - 1, where L=2α 10β 26γ, α ≥ 1, β ≥ 0, γ ≥ 0 are integers. The proposed constructions generate ZCPs with new lengths which cannot be produced by earlier ones.

By interleaving known Z-periodic complementary (ZPC) sequence set, a new ZPC sequence set is constructed with multiple ZPC sequence subsets based on an orthogonal matrix in this work. For this novel ZPC sequence set, which refer to as asymmetric ZPC (AZPC) sequence set, its inter-subset zero cross-correlation zone (ZCCZ) is larger than intra-subset zero correlation zone (ZCZ). In particular, if select a periodic perfect complementary (PC) sequence or PC sequence set and a discrete Fourier transform (DFT) matrix, the resultant sequence set is an inter-group complementary (IGC) sequence set. When a suitable shift sequence is chosen, the obtained IGC sequence set will be optimal in terms of the corresponding theoretical bound. Compared with the existing constructions of IGC sequence sets, the proposed method can provide not only flexible ZCZ width but also flexible choice of basic sequences, which works well in both synchronous and asynchronous operational modes. The proposed AZPC sequence sets are suitable for multiuser environments.

An inter-subset uncorrelated zero-correlation zone (ZCZ) sequence pair set is one consisting of multiple ZCZ sequence pair subsets. What's more, two arbitrary sequence pairs which belong to different subsets should be uncorrelated sequence pairs in this set, i.e., the cross-correlation function (CCF) between arbitrary sequence pairs in different subsets are zeros at everywhere. Meanwhile, each subset is a typical ZCZ sequence pair set. First, a class of uncorrelated ZCZ (U-ZCZ) sequence pair sets is proposed from interleaving perfect sequence pairs. An U-ZCZ sequence pair set is a type of ZCZ sequence pair set, which of most important property is that the CCF between two arbitrary sequence pairs is zero at any shift. Then, a type of inter-subset uncorrelated ZCZ sequence pair set is obtained by interleaving proposed U-ZCZ sequence pair set. In particular, the novel inter-subset uncorrelated ZCZ sequence pair sets are expected to be useful for designing spreading codes for QS-CDMA systems.

An uncorrelated asymmetric ZCZ (UA-ZCZ) sequence set is a special version of an asymmetric ZCZ (A-ZCZ) sequence set, which contains multiple subsets and each subset is a typical ZCZ sequence set. One of the most important properties of UA-ZCZ sequnence set is that two arbitrary sequences from different sequence subsets are uncorrelated sequences, whose cross-correlation function (CCF) is zeros at all shifts. Based on interleaved technique and an uncorrelated sequence set, a new UA-ZCZ sequence set is obtained via interleaving a perfect sequence. The uncorrelated property of the UA-ZCZ sequence sets is expected to be useful for avoiding inter-cell interference of QS-CDMA systems.

The present paper introduces a new approach to the construction of a sequence set with a zero-correlation zone (ZCZ), which is referred to as a ZCZ sequence set. The proposed sequence construction generates a ZCZ sequence set from a ZCZ sequence set. The proposed method can generate an almost optimal ZCZ sequence set, the member size of which approaches the theoretical bound, when an almost optimal ZCZ sequence is used for the sequence construction. The proposed sequence set consists of NO subsets, where a ZCZ sequence set Z(LO, NO, ZO is used in sequence construction. The correlation function of the sequences of a pair of different subsets, referred to as the inter-subset correlation function, has a ZCZ with a width that is about times that of the correlation function of sequences of the same subset (intra-subset correlation function) for integers Λ ≥ 1, T, and m ≥ 0. Wide inter-subset zero-correlation enables improved performance during application of the proposed sequence set.

The even-shift orthogonal sequence whose out-of-phase aperiodic autocorrelation function takes zero at any even shifts is generalized to multi-dimension called even-shift orthogonal array (E-array), and the logic function of E-array of power-of-two length is clarified. It is shown that E-array can be constructed by complementary arrays, which mean pairs of arrays that the sum of each aperiodic autocorrelation function at the same phase shifts takes zero at any shift except zero shift, as well as the one-dimensional case. It is also shown that the number of mates of E-array with which the cross correlation function between E-arrays takes zero at any even shifts is equal to the dimension. Furthermore it is investigated that E-array possesses good aperiodic autocorrelation that the rate of zero correlation values to array length approaches one as the dimension becomes large.

The present paper introduces a new approach to the construction of a sequence set with a zero-correlation zone (ZCZ). This sequence set is referred to as a ZCZ sequence set. The proposed sequence construction generates a ZCZ sequence set from a perfect sequence pair or a single perfect sequence. The proposed method can generate an optimal ZCZ sequence set, the member size of which reaches the theoretical bound.

A novel construction of complementary sequences with multi-width zero cross-correlation zone (ZCCZ) is presented based on the interleaving iteration of a basic kernel set. The presented multi-width ZCCZ complementary (MWZC) sequences can be divided into multiple sequence groups, the correlation functions of which possess one-width intragroup ZCCZ and multi-width intergroup ZCCZ. When an arbitrary orthogonal sequence set with set size equal to sequence length is used as a basic kernel set, the constructed MWZC sequence set and the combination sets of specific subsets with each subset including several groups can be optimal with respect to the theoretical bound on set size. In addition, the MWZC sequence set includes complementary sequence sets with one-width or two-width ZCCZ as special subsets, and allows a more flexible choice of sequence parameters.

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.

The present paper introduces the construction of a class of sequence sets with zero-correlation zones called zero-correlation zone sequence sets. The proposed zero-correlation zone sequence set can be generated from an arbitrary perfect sequence and an arbitrary Golay complementary sequence pair. The proposed construction is a generalization of the zero-correlation zone sequence construction previously reported by the present author. The proposed sequence set can successfully provide CDMA communication without co-channel interference.

The present paper describes a method for the construction of a zero-correlation zone sequence set from a perfect sequence. Both the cross-correlation function and the side-lobe of the auto-correlation function of the proposed sequence sets are zero for phase shifts within the zero-correlation zone. These sets can be generated from an arbitrary perfect sequence, the length of which is the product of a pair of odd integers ((2n+1)(2k+1) for k ≥ 1 and n ≥ 0). The proposed sequence construction method can generate an optimal zero-correlation zone sequence set that achieves the theoretical bounds of the sequence member size given the size of the zero-correlation zone and the sequence period. The peak in the out-of-phase correlation function of the constructed sequences is restricted to be lower than the half of the power of the sequence itself. The proposed sequence sets could successfully provide CDMA communication without co-channel interference, or, in an ultrasonic synthetic aperture imaging system, improve the signal-to-noise ratio of the acquired image.

The present paper introduces an integrated construction of binary sequences having a zero-correlation zone. The cross-correlation function and the side-lobe of the auto-correlation function of the proposed sequence set is zero for the phase shifts within the zero-correlation zone. The proposed method enables more flexible design of the binary zero-correlation zone sequence set with respect to its member size, length, and width of zero-correlation zone. Several previously reported sequence construction methods of binary zero-correlation zone sequence sets can be explained as special cases of the proposed method.

The present paper introduces the construction of a class of sequence sets with zero-correlation zones called zero-correlation zone sequence sets. The proposed zero-correlation zone sequence set can be generated from an arbitrary perfect sequence, the length of which is longer than 4. The proposed sets of ternary sequences, which can be constructed from an arbitrary perfect sequence, can successfully provide CDMA communication without co-channel interference. In an ultrasonic synthetic aperture imaging system, the proposed sequence set can improve the signal-to-noise ratio of the acquired image.

A family of sequences with zero correlation zone, which is shortly called a ZCZ set, can provide CDMA system without co-channel interference nor influence of multipath. This paper presents two types of ZCZ sets of non-binary sequence pairs, which achieve the upper bound of family size for length and zero correlation zone. One, which is produced by use of a perfect complementary pair and an orthogonal code, can change zero correlation zone, while the upper bound is kept. The other, which is generated by use of a newly defined orthogonal pair and an orthogonal code, can offer such CDMA system as a binary ZCZ set seems to be used.

This paper presents constructions of two kinds of sets of sequences with a zero correlation zone, called ZCZ code, which can reach the upper bound of the member size of the sequence set. One is a ZCZ code which can be constructed by a unitary matrix and a perfect sequence. Especially, a ternary perfect sequence with elements 1 and zero can be used to construct the proposed ZCZ code. The other is a ZCZ code of pairs of ternary sequences and binary sequences which can be constructed by an orthogonal matrix that includes a Hadamard matrix and an orthogonal sequence pair. As a special case, an orthogonal sequence pair, which consists of a ternary sequence and a binary sequence, can be used to construct the proposed ZCZ code. These codes can provide CDMA systems without co-channel interference.

This paper presents two kinds of new ZCZ codes consisting of trios of two binary sequences and a bi-phase sequence, which can reach the upper bound on the ZCZ codes. From the viewpoint of sequence design, it is shown that they can provide the most effective ASK-CDMA system, which can remove co-channel interference.

DNA Sequence Design Problem is a crucial problem in information-based biotechnology such as DNA computing. In this paper, we introduce a powerful design strategy for DNA sequences by refining Random Generator. Random Generator is one of the design strategies and offers great advantages, but it is not a good algorithm for generating a large set of DNA sequences. We propose a Two-Step Search algorithm, then show that TSS can generate a larger set of DNA sequences than Random Generator by computer simulation.