# A Direct Construction of Z-Complementary Pairs Using Generalized Boolean Functions

## TL;DR

This paper introduces a new direct method using generalized Boolean functions to construct even-length binary Z-complementary pairs with a higher ZCZ ratio of 3/4, improving interference reduction in communication systems.

## Contribution

The paper presents a novel direct construction of EB-ZCPs using GBFs achieving a ZCZ ratio of 3/4, surpassing the previous maximum of 2/3.

## Key findings

- Achieves a ZCZ ratio of 3/4 for EB-ZCPs
- Constructs sequences of length 2^{m-1}+2
- Provides explicit formulas for ZCZ width and sequence length

## Abstract

The zero correlation zone (ZCZ) ratio, i.e., the ratio of the width of the ZCZ and the length of the sequence plays a major role in reducing interference in an asynchronous environment of communication systems. However, to the best of the author's knowledge, the highest ZCZ ratio for even-length binary Z-complementary pairs (EB-ZCPs) which are directly constructed using generalized Boolean functions (GBFs), is $\frac{2}{3}$. In this research, we present a direct construction of EB-ZCPs through GBFs, which can achieve a ZCZ ratio of $\frac{3}{4}$. In general, the constructed EB-ZCPs are of length $2^{m-1}+2$, having a ZCZ width of $2^{m-2}+2^{\pi(m-3)}+1$ where pi is a permutation over $m-2$ variables.