A unified construction of type-Ⅰ even length Z-complementary pairs based on generalized Boolean function

Abstract

Constructions of Z-complementary pairs (ZCPs) using generalized Boolean functions (GBFs) have a very rich literature. However, these works only focus on ZCPs having lengths with specific forms. In this paper, we propose a unified framework to construct q-phase ZCPs based on GBFs, which can obtain the algebraic structure of Type-I ZCPs of any even length. Through the proposed unified framework, we can propose several direct constructions of even-length ZCPs, which are not reported before. Also, all the previous constructions of Type-I ZCPs of even length based on GBFs, can be seen as special cases of the proposed construction.