Zero-Difference Balanced Functions With Applications
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Zero-difference balanced functions introduced recently are an interesting subject of study, as they unify difference sets, permutation polynomials, perfect nonlinear functions, planar functions, and semifields, and have applications in combinatorics, coding theory, cryptography, and finite geometry. In this article, we give a well-rounded treatment of zero-difference balanced functions. We survey known zero-difference balanced functions, construct new ones, and summarize some of their applications.
Key-wordsConstant composition codes Difference families Difference systems of sets Perfect nonlinear functions Permutation functions Zero-difference balanced functions
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