Abstract
Zero-difference balanced (ZDB) functions are a generalization of perfect nonlinear functions, and have received a lot of attention due to their important applications in coding theory, cryptography, combinatorics and some engineering areas. In this paper, based on cyclotomy and generalized cyclotomy, a construction of a partitioned difference family is presented, and then a class of ZDB functions is obtained. In addition, these ZDB functions are applied to construct optimal constant composition codes and optimal and perfect difference systems of sets.
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