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Zero-Difference Balanced Functions With Applications

  • Cunsheng Ding
  • Yin Tan
Article

Abstract

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.

05A10 14H05 

Key-words

Constant composition codes Difference families Difference systems of sets Perfect nonlinear functions Permutation functions Zero-difference balanced functions 

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Copyright information

© Grace Scientific Publishing 2012

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringHong Kong University of Science and TechnologyKowloonHong Kong
  2. 2.Division of Mathematical SciencesSchool of Physical & Mathematical SciencesSingapore

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