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

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发表日期：

2024年7月12日

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Piyush Priyanshu,
Subhabrata Paul,
Sudhan Majhi

摘要

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) $ $(N_{1} \times 2^{m}, N_{1} \times 2^{m} - (N_{1} - 1) / 2)$ -ZCP, where $N_1$ $N_{1}$ is an odd positive integer greater than 1, and $m\ge 1$ $m \geq 1$ . For $N_1=3$ $N_{1} = 3$ , the result produces Z-optimal type-II ZCP of length $3\times 2^m$ $3 \times 2^{m}$ . 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) $ $(N_{2} \times 2^{m}, N_{2} \times 2^{m} - (N_{2} - 2) / 2)$ -ZCP, where $N_2$ $N_{2}$ is an even positive integer greater than 1, and $m\ge 1$ $m \geq 1$ . For $N_2=2$ $N_{2} = 2$ and $N_2=4$ $N_{2} = 4$ , the result provides a Golay complementary pair (GCP) of length $2^{m+1}$ $2^{m + 1}$ and Z-optimal type-II ZCP of length $2^{m+2}$ $2^{m + 2}$ . 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.