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.

翻译：本文提出了一类新的基于广义布尔函数与两个单位根的叉$Z$互补对（CZCP）。我们的核心思想是考虑集合$\{1,2,\cdots, n\}$的任意划分，其中两个子集分别对应给定的两个单位根，由此获得由这两个单位根决定的新字母表长度的两个截断序列。我们证明这两个截断序列构成一类具有灵活序列长度和大零相关区宽度的新型$q$元CZCP。进一步，通过考虑划分的第二类斯特林数推导出枚举公式，并证明相较于现有工作，所构造CZCP的数量显著增加。