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.

Based on trace function over finite field GF(pn ), new construction of generalized Hadamard matrices with order pn is presented, where p is prime and n is even. The rows in new generalized Hadamard matrices are cyclically distinct and have large linear span, which greatly improves the security of the system employing them as spreading sequences.

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 letter, we present quasi-Jacket block matrices over GF(2), i.e., binary matrices which all are belong to a class of cocyclic matrices. These matrices are may be useful in digital signal processing, CDMA, and coded modulation. Based on Circular Permutation Matrix (CPM) cocyclic quasi-Jacket block low-density matrix is introduced in this letter which is useful in coding theory. Additionally, we show that the fast algorithm of quasi-Jacket block matrix.

In this letter, we define the generalized doubly stochastic processing via Jacket matrices of order-2n and 2n with the integer, n≥2. Different from the Hadamard factorization scheme, we propose a more general case to obtain a set of doubly stochastic matrices according to decomposition of the fundaments of Jacket matrices. From order-2n and order-2n Jacket matrices, we always have the orthostochastoc case, which is the same as that of the Hadamard matrices, if the eigenvalue λ1 = 1, the other ones are zeros. In the case of doubly stochastic, the eigenvalues should lead to nonnegative elements in the probability matrix. The results can be applied to stochastic signal processing, pattern analysis and orthogonal designs.

The present paper introduces a new construction of a class of binary sequence set having a zero-correlation zone (hereafter binary zcz sequence set). 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. This paper shows that such a construction generates a binary zcz sequence set from an arbitrary pair of Hadamard matrices of common size. Since the proposed sequence construction generates a sequence set from an arbitrary pair of Hadamard matrices, many more types of sequence sets can be generated by the proposed sequence construction than is possible by a sequence construction that generates sequence sets from a single arbitrary Hadamard matrix.