  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.
