Mutually orthogonal complementary sets (MOCSs) have found a number of practical applications in wireless communications and radar owing to their perfect aperiodic auto-correlation and cross-correlation properties. Recently, toward the challenge of designing MOCSs with non-power-of-two lengths, direct constructions were presented by Wu et al. using generalized Boolean functions (GBFs). In this letter, a new construction of MOCSs is proposed based on GBFs, which leads to MOCSs with flock size 2k+1and length 2m+ 2t, whose set size is 1/2 of the flock size, where integers 0 ≤ t <; k ≤ m. In addition, the constructed MOCSs can yield column sequence peak-to-mean envelope power ratio (PMEPR) of at most 2.

Z-complementary code sets (ZCCSs), extended from complete complementary codes (CCCs), have ideal correlations within a zone around the in-phase position named zero correlation zone (ZCZ). In this article, two classes of aperiodic ZCCSs with good cross-correlation subsets are investigated. They are multiple CCCs with inter-set zero cross-correlation zone (ZCCZ) property and multiple aperiodic ZCCSs with ideal inter-set aperiodic cross-correlation property respectively, the latter is referred to as an aperiodic inter-group complementary (IGC) code set and each ZCCS is called a group. First of all, based on polyphase paraunitary (PU) matrices and special permutation matrices, a construction of multiple polyphase CCCs with an inter-set ZCCZ is proposed. The obtained multiple CCCs have potential applications in interference-free multi-cell environments to support a large number of users. In addition, a construction of aperiodic polyphase IGC code sets is presented from polyphase PU matrices. We remark that different groups of the derived IGC code sets yield different constituent sequence lengths, thus they could provide a variety of quality of service (QoS) in quasi-synchronous multi-cell multi-rate communication systems. To the best of our knowledge, the aforementioned constructions of ZCCSs with good cross-correlation subsets based on PU matrices have not been reported in the literature.

Recently, quasi-complementary sequence sets (QCSSs) including low correlation zone complementary sequence sets (LCZ-CSSs), and low correlation complementary sequence sets (LC-CSSs) have raised lots of concerns. According to the theoretical bounds, the set size of a QCSS is much larger than that of a traditional perfect complementary sequence set (PCSS). As a result, it is believed that QCSSs have potential applications in multi-carrier code-division multiple-access (MC-CDMA) systems to support more users. As binary sequences are desired in practice because of easier realization, we consider the design of binary QCSSs with large set size in this letter. A construction of aperiodic binary LCZ-CSSs is proposed, which leads to aperiodic binary LCZ-CSSs with asymptotically optimal parameters. Additional, aperiodic binary LC-CSSs with asymptotically optimal parameters can also be derived from the proposed construction.

Spectrally-constrained sequences (SCSs) with good correlation properties, and low spectral power under the spectral constraint have found many practical applications in communication, and radar systems operating over non-contiguous carriers or frequency slots. In this letter, a construction of single-channel spectrally-null-constrained sequence (SNCS) families with good correlation is proposed. Following the proposed construction, a single-channel polyphase SNCS family with period N(N + 1), and family size (p - 1) can be obtained, which has zero power leakage underthe spectral constraint{1 + a(N + 1) : a ∈ ℤN}, where N is an odd integer, and p is the minimum prime factor of N. Note that the maximum periodic correlation magnitude of the derived single-channel SNCS family is (N + 1), which asymptotically achieves the correlation lower bound as p increasing.

Complete complementary codes (CCCs) have found a number of practical applications in wireless communications owing to their perfect aperiodic auto-correlation and cross-correlation properties. In particular, an important application of CCCs is in interference-free multi-carrier code-division multiple-access (MC-CDMA) systems. The available number of complementary codes determines the system capacity. To enlarge the system capacity, this paper focuses on constructing multiple CCCs with inter-set zero cross-correlation zone (ZCCZ) property based on generalized Boolean functions (GBFs). To the best of our knowledge, such multiple CCCs have not been reported in the literature. The obtained multiple CCCs can provide advantages in applications to MC-CDMA systems with multiple cells. As a byproduct, optimal aperiodic Z-complementary code sets (ZCCSs) with low peak-to-mean envelope power ratio (PMEPR) can be derived by combining these CCCs.

Complementary sequences have been applied to multi-carrier code-division multiple-access wireless communication systems. In this letter, multiple complementary sequence sets are constructed. The presented multiple complementary sequence sets have the following properties: first, each set is a complete complementary code (CCC) with parameters (p,p,p)-CCC; second, the maximum inter-set aperiodic cross-correlation amplitude is p; and finally, an aperiodic quasi-complementary sequence set with asymptotically near optimal correlation amplitude will be obtained by combining these complementary sequence sets together, which is not covered in the literature.

Codebooks with small inner product correlation have wide applications in many fields, such as direct spread code-division multiple access communications, signal processing, and compressed sensing. It is extremely hard to produce optimal codebooks with respect to the Welch bound or the Levenstein bound. This letter focuses on constructing asymptotically optimal codebooks with additive characters of finite fields. Following the proposed constructions, two classes of asymptotically optimal codebooks with respect to the Welch bound are obtained. In addition, the resulting codebooks could have a small alphabet size.

An (M, K, N, δmax)-quasi-complementary sequence set (QCSS) is referred to as a set of M two-dimensional matrices of size K × N with maximum periodic correlation magnitude δmax. It can be applied to a multi-carrier code-division multiple-access communication system to achieve low-interference performance. Compared with perfect complementary sequence sets, QCSSs with maximum periodic correlation magnitudes achieving or asymptotically achieving the correlation lower bounds have the advantage of supporting more users. In this paper, two constructions of periodic QCSSs from additive characters and multiplicative characters of finite fields are developed. In the first construction, new QCSSs with constituent sequence length N = p are proposed by using cyclic classes, where p is a prime. In the second construction, QCSSs with constituent sequence length N = q - 1 and N = r2- 1 are presented by employing almost difference sets and special sets proposed by Katz, respectively, where q > 5 is an odd prime power and r is a prime power. Notably, the parameters of QCSSs derived from the second construction are flexible and have not been covered in the literature. In addition, all the proposed periodic QCSSs are asymptotically optimal with respect to the correlation lower bounds.

Mutually orthogonal complementary codes have found many practical applications in wireless communications owing to their perfect correlation properties. However, the set size of a mutually orthogonal complementary code set (MOCCS) is upper bounded by the number of constituent sequences in each complementary code. As a result, the number of users in the communication system is limited. To overcome this limitation, quasi-complementary sequence sets (QCSSs) were proposed, which include low correlation zone complementary sequence sets (LCZ-CSSs) and low correlation complementary sequence sets (LC-CSSs). In this paper, aperiodic quasi-complementary sequences are our main interest. Constructions of aperiodic LC-CSSs and aperiodic LCZ-CSSs over the complex roots of unity are proposed. With these constructions, asymptotically optimal aperiodic QCSSs can be obtained.

An$(\boldsymbol {M},\boldsymbol {K},\boldsymbol {N},\delta _{\max })$-quasi-complementary sequence set (QCSS) is referred to as a set of$\boldsymbol {M}$2-D matrices of order$\boldsymbol {K}\times \boldsymbol {N}$with periodic tolerance$\delta _{\max }$. In a multicarrier code-division multiple-access (MC-CDMA) communication system, the set size$\boldsymbol {M}$of a QCSS is equal to the maximum number of users it can support, and the periodic tolerance$\delta _{\max }$determines the interference performance. For the application of a QCSS, it is desirable that the set size should be as large as possible, and the periodic tolerance should be as small as possible. In this paper, a framework of a periodic QCSS is proposed from additive and multiplicative characters associated with a specific integer set. It is then discovered that the parameters of the obtained QCSS are determined by the employed integer set. From this discovery, new classes of periodic QCSSs with large set sizes and low periodic tolerances are constructed and associated with some known integer sets.

In this paper, we build a family of chameleon hash functions and strongly unforgeable one-time signature schemes based on the intractability assumption of the discrete logarithm problem (DLP) over inner automorphism groups. Since the DLP assumption over inner automorphism groups does not admit sub-exponential attacks, thus the sizes of the working parameters used in our constructions are shorten significantly. This leads to remarkable gains for our proposals both in running time and in storage space. In addition, as far as we know, this is the first time to build CHF and OTS based on noncommutative groups.

A pair of binary sequences is generalized from the concept of a two-level autocorrelation function of a single binary sequence. In this paper, new families of binary sequence pairs with period N = np, where gcd(n,p) = 1, and optimal correlation values -1 are constructed, as well as new families of binary sequence pairs with three-level correlation and period N≡0(mod 4). For the new binary sequence pairs with optimal correlation values, their corresponding new difference set pairs and almost difference set pairs are also derived.

The following results are proven in this paper: 1) neither periodic autonor cross-correlation of the truncated Costas optical orthogonal code (TC OOC) is upper bounded by 1; 2) TC OOC is a class of (/spl omega/(2p-3), /spl omega/,2,2) optical orthogonal codes.