Han Cai, Zhengchun Zhou, Xiaohu Tang, Ying Miao: Zero-Difference Balanced Functions With New Parameters and Their Applications

Journal:IEEE Transactions on Information Theory

Abstract:As an optimal combinatorial object, zero-difference balanced (ZDB) functions introduced by Ding in 2008, are a generalization of the well-known perfect nonlinear functions. ZDB functions have received much attention in recent years due to its important applications in coding theory and sequence design. One objective of this paper is to present a construction of ZDB functions based on a kind of generalized cyclotomy. It generates ZDB functions over cyclic group with new parameters which can not be produced by earlier constructions. Another objective of this paper is to employ these ZDB functions to obtain at the same time: 1) optimal constant-composition codes; 2) perfect difference systems of sets; and 3) optimal frequency-hopping sequences, all with new parameters.

Indexed by:SCI

Volume:63

Issue:7

Page Number:4379-4387

Translation or Not:no

Date of Publication:2017-07-15

Links to published journals:https://ieeexplore.ieee.org/document/7865985