  Zero-difference balanced (ZDB) functions can be employed in many
applications, e.g., optimal constant composition codes, optimal and perfect
difference systems of sets, optimal frequency hopping sequences, etc. In this
paper, two results are summarized to characterize ZDB functions, among which a
lower bound is used to achieve optimality in applications and determine the
size of preimage sets of ZDB functions. As the main contribution, a generic
construction of ZDB functions is presented, and many new classes of ZDB
functions can be generated. This construction is then extended to construct a
set of ZDB functions, in which any two ZDB functions are related uniformly.
Furthermore, some applications of such sets of ZDB functions are also
introduced.
