Root Cross Z-Complementary Pairs with Large ZCZ Width

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.