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.
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