In this letter, we propose a novel direct construction of three-phase Z-complementary triads with flexible lengths and various widths of the zero-correlation zone based on extended Boolean functions. The maximum width ratio of the zero-correlation zone of the construction can reach 3/4. And the proposed sequences can exist for all lengths other than powers of three. We also investigate the peak-to-average power ratio properties of the proposed ZCTs.

This letter presents a novel tensor voting mechanism — analytic tensor voting (ATV), to get rid of the difficulties in original tensor voting, especially the efficiency. One of the main advantages is its explicit voting formulations, which benefit the completion of tensor voting theory and computational efficiency. Firstly, new decaying function was designed following the basic spirit of decaying function in original tensor voting (OTV). Secondly, analytic stick tensor voting (ASTV) was formulated using the new decaying function. Thirdly, analytic plate and ball tensor voting (APTV, ABTV) were formulated through controllable stick tensor construction and tensorial integration. These make the each voting of tensor can be computed by several non-iterative matrix operations, improving the efficiency of tensor voting remarkably. Experimental results validate the effectiveness of proposed method.

In this letter, the almost binary sequence (sequence with a single zero element) is considered as a special class of binary sequence. Four new bounds on the cross-correlation of balanced (almost) binary sequences with period Q ≡ 1(mod 4) under the precondition of out-of-phase autocorrelation values {-1} or {1, -3} are firstly presented. Then, seven new pairs of balanced (almost) binary sequences of period Q with ideal or optimal autocorrelation values and meeting the lower cross-correlation bounds are proposed by using cyclotomic classes of order 4. These new bounds of (almost) binary sequences with period Q achieve smaller maximum out-of-phase autocorrelation values and cross-correlation values.

The concept of Gaussian integer sequence pair is generalized from a single Gaussian integer sequence. In this letter, by adopting cyclic difference set pairs, a new construction method for perfect Gaussian integer sequence pairs is presented. Furthermore, the necessary and sufficient conditions for constructing perfect Gaussian integer sequence pairs are given. Through the research in this paper, a large number of perfect Gaussian integer sequence pairs can be obtained, which can greatly extend the existence of perfect sequence pairs.

This letter provides a direct construction of binary even-length Z-complementary pairs. To date, the maximum zero correlation zone ratio of Type-I Z-complementary pairs has reached 6/7, but no direct construction of Z-complementary pairs can achieve the zero correlation zone ratio of 6/7. In this letter, based on Boolean function, we give a direct construction of binary even-length Z-complementary pairs with zero correlation zone ratio 6/7. The length of constructed Z-complementary pairs is 2m+3 + 2m + 2+2m+1 and the width of zero correlation zone is 2m+3 + 2m+2.

Two new families of balanced almost binary sequences with a single zero element of period L=2q are presented in this letter, where q=4d+1 is an odd prime number. These sequences have optimal autocorrelation value or optimal autocorrelation magnitude. Our constructions are based on cyclotomy and Chinese Remainder Theorem.