Zero-Difference Balanced Functions With New Parameters and Their Applications

Cai, Han; Zhou, Zhengchun; Tang, Xiaohu; Miao, Ying

doi:10.1109/tit.2017.2675441

Cited by 15 publications

(16 citation statements)

References 30 publications

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“…Remark 2. Corollary 1 is the same as Theorem 1 in [10]. So Theorem 1 in this paper can be viewed as a generalization of Theorem 1 in [10].…”

Section: One Construction Of Zdb Functionsmentioning

confidence: 83%

“…, e − 1]) en−1 e−1 +1 CCC. To compare the parameters of some known optimal CCCs, the reader is referred to Table II in [10].…”

Section: Optimal Constant Composition Codesmentioning

confidence: 99%

“…The optimal DSSs constructed in this paper are partitioned-type. To compare the parameters of some known partitioned-type optimal DSSs, the reader is referred to Table III in [10].…”

Section: Optimal and Perfect Difference Systems Of Setsmentioning

confidence: 99%

“…The main contribution of the letter are twofold. Firstly, by generalizing the construction of ZDB functions proposed by Cai et al [10], ZDB functions can be obtained over Z e × k i=0 F q i . Secondly, it shows that all the known ZDB functions using cyclotomic cosets over Z n [6,7,8], are indeed special cases of the generic construction in [12].…”

Section: Introductionmentioning

confidence: 99%

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A Note on Two Constructions of Zero-Difference Balanced Functions

Tang

et al. 2019

IEICE Trans. Fundamentals

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Notes on two constructions of zero-difference balanced (ZDB) functions are made in this letter. Then ZDB functions over Z e × k i=0 F q i are obtained. And it shows that all the known ZDB functions using cyclotomic cosets over Z n are special cases of a generic construction. Moreover, applications of these ZDB functions are presented. key words: constant composition code, constant weight code, difference system of sets, frequency-hopping sequence, zero-difference balanced function

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“…Remark 2. Corollary 1 is the same as Theorem 1 in [10]. So Theorem 1 in this paper can be viewed as a generalization of Theorem 1 in [10].…”

Section: One Construction Of Zdb Functionsmentioning

confidence: 83%

“…, e − 1]) en−1 e−1 +1 CCC. To compare the parameters of some known optimal CCCs, the reader is referred to Table II in [10].…”

Section: Optimal Constant Composition Codesmentioning

confidence: 99%

“…The optimal DSSs constructed in this paper are partitioned-type. To compare the parameters of some known partitioned-type optimal DSSs, the reader is referred to Table III in [10].…”

Section: Optimal and Perfect Difference Systems Of Setsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Note on Two Constructions of Zero-Difference Balanced Functions

Tang

et al. 2019

IEICE Trans. Fundamentals

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“…More recently, the cyclotomy has proved to be valuable in other applied fields such as sequences [40,15,8,22,9], coding theory [15,17,16,10,25] and cryptography [15]. The combinatorics has also benefited from the use of cyclotomy, which can be applied for constructing difference sets, difference families, and so on [32,35,17,41,36,7,39,34,37,6,29].…”

Section: Introductionmentioning

confidence: 99%

Three classes of partitioned difference families and their optimal constant composition codes

Xu¹,

Qu²,

Cao³

2022

AMC

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<p style='text-indent:20px;'>Cyclotomy, firstly introduced by Gauss, is an important topic in Mathematics since it has a number of applications in number theory, combinatorics, coding theory and cryptography. Depending on <inline-formula><tex-math id="M2">\begin{document}$ v $\end{document}</tex-math></inline-formula> prime or composite, cyclotomy on a residue class ring <inline-formula><tex-math id="M3">\begin{document}$ {\mathbb{Z}}_{v} $\end{document}</tex-math></inline-formula> can be divided into classical cyclotomy or generalized cyclotomy. Inspired by a foregoing work of Zeng et al. [<xref ref-type="bibr" rid="b40">40</xref>], we introduce a generalized cyclotomy of order <inline-formula><tex-math id="M4">\begin{document}$ e $\end{document}</tex-math></inline-formula> on the ring <inline-formula><tex-math id="M5">\begin{document}$ {\rm GF}(q_1)\times {\rm GF}(q_2)\times \cdots \times {\rm GF}(q_k) $\end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id="M6">\begin{document}$ q_i $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M7">\begin{document}$ q_j $\end{document}</tex-math></inline-formula> (<inline-formula><tex-math id="M8">\begin{document}$ i\neq j $\end{document}</tex-math></inline-formula>) may not be co-prime, which includes classical cyclotomy as a special case. Here, <inline-formula><tex-math id="M9">\begin{document}$ q_1 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M10">\begin{document}$ q_2 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M11">\begin{document}$ \cdots $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M12">\begin{document}$ q_k $\end{document}</tex-math></inline-formula> are powers of primes with an integer <inline-formula><tex-math id="M13">\begin{document}$ e|(q_i-1) $\end{document}</tex-math></inline-formula> for any <inline-formula><tex-math id="M14">\begin{document}$ 1\leq i\leq k $\end{document}</tex-math></inline-formula>. Then we obtain some basic properties of the corresponding generalized cyclotomic numbers. Furthermore, we propose three classes of partitioned difference families by means of the generalized cyclotomy above and <inline-formula><tex-math id="M15">\begin{document}$ d $\end{document}</tex-math></inline-formula>-form functions with difference balanced property. Afterwards, three families of optimal constant composition codes from these partitioned difference families are obtained, and their parameters are also summarized.</p>

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Two classes of optimal frequency-hopping sequences with new parameters

Cao

et al. 2018

AAECC

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Zero-Difference Balanced Functions With New Parameters and Their Applications

Cited by 15 publications

References 30 publications

A Note on Two Constructions of Zero-Difference Balanced Functions

A Note on Two Constructions of Zero-Difference Balanced Functions

Three classes of partitioned difference families and their optimal constant composition codes

Two classes of optimal frequency-hopping sequences with new parameters

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