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A new construction of zero-difference balanced functions and two applications

  • Junying Liu
  • Yupeng Jiang
  • Qunxiong ZhengEmail author
  • Dongdai Lin
Article
  • 24 Downloads

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.

Keywords

Zero-difference balanced function Cyclotomy Generalized cyclotomy Constant composition code Difference system of sets 

Mathematics Subject Classification

05A10 11T22 11T71 

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No.61402524, No.11701553, No.61872383). The work of Jiang Yupeng was also supported by Foundation of Science and Technology on Information Assurance Laboratory (61421120102162112007). The work of Zheng Qunxiong was also supported by National Postdoctoral Program for Innovative Talents (BX201600188) and by China Postdoctoral Science Foundation funded project (2017M611035) and by Young Elite Scientists Sponsorship Program by CAST (2016QNRC001).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Information Security, Institute of Information EngineeringChinese Academy of SciencesBeijingChina
  2. 2.School of Cyber SecurityUniversity of Chinese Academy of SciencesBeijingChina
  3. 3.State Key Laboratory of CryptologyBeijingChina
  4. 4.National Digital Switching System Engineering & Technological Research CenterZhengzhouChina

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