A Direct Construction of Asymptotically Optimal Type-II ZCP for Every Possible Even Length

A pair of the complex-valued sequences is called a Z-complementary pair (ZCP) if it has zero aperiodic auto-correlation sum (AACS) for all time-shifts within a certain region, commonly known as zero correlation zone (ZCZ). Type-II ZCPs have the ZCZ around the end time shifts position. Till the date, no direct construction technique is available for type-II ZCPs of length non-power-of-two. For the first time, we have advocated a direct construction of 2
^h
-ary (h∈\mathbb N) type-II ZCPs of length 2
^m
P with ZCZ width 2
^m
P$+1-$P, where m and P are positive integers, using the multivariable function. The proposed type-II ZCPs feature the optimal case, i.e., Z≤N$-$1 for the lengths in the form of power-of-two and asymptotically optimal for other even lengths.