On Generalized Zero-Difference Balanced Functions

J, Lin; Liao, Qunying

doi:10.4134/ckms.2016.31.1.041

Cited by 5 publications

(6 citation statements)

References 14 publications

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“…To generalize the concept of ZDBF, in [34] the authors recently proposed a concept called zero-difference function (ZDF) instead of a concept called generalized zero-difference balanced function (G-ZDBF). Since the concept of G-ZDBF [18] would lead to the misunderstanding that such G-ZDBF are really ''balanced''. Thus the concept of zero-difference (ZD) is preferred.…”

Section: Function Is Called An (N M S) Zero-difference Function (Zdf) If It Is (N M S) Zerodifference a Zdf Is Cyclic If The Group (A +) mentioning

confidence: 99%

“…Thus the concept of zero-difference (ZD) is preferred. Some ZDFs are constructed following the directions of ZDBFs (see [17], [18], [24], [32] and the references therein). However the DSSs and FHSs from ZDFs are not always as good as those from ZDBFs.…”

Section: Function Is Called An (N M S) Zero-difference Function (Zdf) If It Is (N M S) Zerodifference a Zdf Is Cyclic If The Group (A +) mentioning

confidence: 99%

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

Tang

2019

IEEE Access

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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. INDEX TERMSDifference system of sets, frequency-hopping sequence, zero-difference balanced function, zero-difference function. I. INTRODUCTION Difference systems of sets (DSS) are related with comma-free codes [21], [29], authentication codes and secrete sharing schemes [15], [27]. Frequency-hopping sequences are used to reduce the interferes between the wireless devices in CDMA communication [6], [11], [12], [14]. Definition 1 [8]: Let (A, +) and (B, +) be two finite Abelian groups. 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, |{x ∈ A | f (x + a) − f (x) = 0}| = λ, where n = |A| and m = |f (A)|. Ding first proposed the concept of ZDBF in 2008 [8], [8]. Since optimal DSSs and FHSs can be obtained from ZDBFs, many researchers have been working on constructing ZDBFs (see [3]-[5], [8], [9], [13], [22], [31], [33], [35], [37]-[39] and the references therein). It is worth mentioning that in The associate editor coordinating the review of this article and approving it for publication was Zilong Liu.

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Section: Function Is Called An (N M S) Zero-difference Function (Zdf) If It Is (N M S) Zerodifference a Zdf Is Cyclic If The Group (A +) mentioning

confidence: 99%

Section: Function Is Called An (N M S) Zero-difference Function (Zdf) If It Is (N M S) Zerodifference a Zdf Is Cyclic If The Group (A +) mentioning

confidence: 99%

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

Tang

2019

IEEE Access

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“…Any (n, m, λ) ZDBF is differentially λ-vanishing. But there had been little research on this concept, until Jiang and Liao proposed a related concept called generalized zero-difference balanced function in 2016 [12].…”

Section: Introductionmentioning

confidence: 99%

Some Zero-Difference Functions Over $\mathbb{Z}_n$ Using Cyclotomies

2019

Preprint

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“…Any (n, m, λ) ZDB function is differentially λ-vanishing (λ-DV). But there had been little research on this concept, until Jiang and Liao proposed a related concept called generalized zero-difference balanced (G-ZDB) function in 2016 [26]. A function from A onto B is an (n, m, S ) generalized zero-difference balanced function, if there exists a constant set S ⊂ N such that for any nonzero element a ∈ A * ,…”

Section: Introductionmentioning

confidence: 99%

“…where n = |A| and m = | f (A)|. Then some objects can be obtained by G-ZDB functions [25,26,33], but they are not optimal. The main reason is that the size of S is too large, which implies they are not really zero-difference balanced.…”

Section: Introductionmentioning

confidence: 99%

The Zero-Difference Properties of Functions and Their Applications

Yi,

Pei

2018

Preprint

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A function f from an Abelian group (A, +) to an Abelian group (B,where λ is a constant number. ZDB functions have many good applications. However it is point out that many known zero-difference balanced functions are already given in the language of partitioned difference family (PDF). The problem that whether zero-difference "not balanced" functions still have good applications as ZDB functions, is investigated in this paper. By using the change point technic, zero-difference functions with good applications are constructed from known ZDB function. Then optimal difference systems of sets (DSS) and optimal frequency-hopping sequences (FHS) are obtained with new parameters. Furthermore the sufficient and necessary conditions of these being optimal, are given.

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On Generalized Zero-Difference Balanced Functions

Cited by 5 publications

References 14 publications

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

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

Some Zero-Difference Functions Over $\mathbb{Z}_n$ Using Cyclotomies

The Zero-Difference Properties of Functions and Their Applications

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