Construction of all even lengths type-II Z-complementary pair with a large zero-correlation zone

Abstract

This paper presents a direct construction of type-II Z-complementary pair (ZCP) of q-ary (q is even) for all even lengths with a wide zero-correlation zone (ZCZ). The proposed construction provides type-II \(\left( N_1\times 2^m, N_1\times 2^m-\left( N_1-1\right) /2\right) \)-ZCP, where \(N_1\) is an odd positive integer greater than 1, and \(m\ge 1\). For \(N_1=3\), the result produces Z-optimal type-II ZCP of length \(3\times 2^m\). In this paper, we also present a construction of type-II \(\left( N_2\times 2^m, N_2\times 2^m-\left( N_2-2\right) /2\right) \)-ZCP, where \(N_2\) is an even positive integer greater than 1, and \(m\ge 1\). For \(N_2=2\) and \(N_2=4\), the result provides a Golay complementary pair (GCP) of length \(2^{m+1}\) and Z-optimal type-II ZCP of length \(2^{m+2}\). Both the proposed constructions are compared with the existing state-of-the-art, and it has been observed that it produces a large ZCZ, which covers all existing work in terms of lengths.