Root Cross Z-Complementary Pairs with Large ZCZ Width

TL;DR

This paper introduces a new family of cross Z-complementary pairs (CZCPs) using generalized Boolean functions and roots of unity, achieving flexible lengths and large zero-correlation zones, with a significant increase in the number of such pairs.

Contribution

The paper proposes a novel construction of CZCPs based on arbitrary partitions and roots of unity, expanding the available sequence lengths and the quantity of CZCPs.

Findings

Constructed CZCPs with flexible lengths and large ZCZ width.

Derived an enumeration formula showing increased number of CZCPs.

Demonstrated the effectiveness of the new construction method.

Abstract

In this paper, we present a new family of cross $Z$-complementary pairs (CZCPs) based on generalized Boolean functions and two roots of unity. Our key idea is to consider an arbitrary partition of the set $\{1,2,\cdots, n\}$ with two subsets corresponding to two given roots of unity for which two truncated sequences of new alphabet size determined by the two roots of unity are obtained. We show that these two truncated sequences form a new $q$-ary CZCP with flexible sequence length and large zero-correlation zone width. Furthermore, we derive an enumeration formula by considering the Stirling number of the second kind for the partitions and show that the number of constructed CZCPs increases significantly compared to the existing works.