More Optimal Difference Systems of Sets and Frequency-Hopping Sequences From Zero-Difference Functions

Zongxiang Yi,Chunming Tang

doi:10.1109/access.2019.2935254

Abstract

Difference systems of sets (DSS) and frequency-hopping sequences (FHS) are two objects with many applications in wireless communication. Zero-difference balanced function (ZDBF) and near zero-difference balanced functions (NZDBF) are two types of functions which can be used to obtain optimal DSSs and FHSs. In order to obtain more optimal DSSs and FHSs, zero-difference function (ZDF) as a generalization of ZDBF and NZDBF was recently proposed. In this paper, four classes of ZDFs with good applications are given from some known ZDBFs. It is noticed that these ZDFs are neither ZDBFs nor NZDBFs. As a result, more optimal DSSs and FHSs with new flexible parameters are obtained.

Highlights

Difference systems of sets (DSS) are related with comma-free codes [21], [29], authentication codes and secrete sharing schemes [15], [27]
Since optimal DSSs and frequency-hopping sequences (FHS) can be obtained from zero-difference balanced function (ZDBF), many researchers have been working on constructing ZDBFs
This paper aims to obtain more optimal DSSs and FHSs with new flexible parameters from new zero-difference function (ZDF)

Summary

INTRODUCTION

Difference systems of sets (DSS) are related with comma-free codes [21], [29], authentication codes and secrete sharing schemes [15], [27]. A function from A to B is an (n, m, λ) zero-difference balanced function (ZDBF), if there exists a constant number λ such that for any nonzero element a ∈ A,. Some ZDFs are constructed following the directions of ZDBFs (see [17], [18], [24], [32] and the references therein). Following the direction in [34], four classes of ZDFs are constructed from the ZDBFs in [35] which generalize the results in [4], [32]. TWO CLASSES OF KNOWN ZERO-DIFFERENCE BALANCED FUNCTIONS In this subsection, we will recall some results in [33], [35]. The former has more applications while the later gives more flexible parameters For the former, let C1(n, e) denote these conditions:.

SOME CLASSES OF ZERO-DIFFERENCE FUNCTIONS

CONCLUSION