A new construction of zero-difference balanced functions and two applications
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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.
KeywordsZero-difference balanced function Cyclotomy Generalized cyclotomy Constant composition code Difference system of sets
Mathematics Subject Classification05A10 11T22 11T71
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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