A Note on Two Constructions of Zero-Difference Balanced Functions

Abstract: Notes on two constructions of zero-difference balanced (ZDB) functions are made in this letter. Then ZDB functions over $\mathbb{Z}{e}\times \prod{i=0}^{k}{\mathbb{F}_{q_i}}$ are obtained. And it shows that all the known ZDB functions using cyclotomic cosets over $\mathbb{Z}_{n}$ are special cases of a generic construction. Moreover, applications of these ZDB functions are presented.