A new construction of zero-difference balanced functions and two applications

Junying Liu; Yupeng Jiang; Qunxiong Zheng; Dongdai Lin

doi:10.1007/s10623-019-00616-x

A new construction of zero-difference balanced functions and two applications

Junying Liu
, Yupeng Jiang
, Qunxiong Zheng^*
, Dongdai Lin

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	2251-2265
Number of pages	15
Journal	Designs, Codes, and Cryptography
Volume	87
Issue number	10
DOIs	https://doi.org/10.1007/s10623-019-00616-x
State	Published - 1 Oct 2019
Externally published	Yes

Keywords

Constant composition code
Cyclotomy
Difference system of sets
Generalized cyclotomy
Zero-difference balanced function

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10.1007/s10623-019-00616-x

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title = "A new construction of zero-difference balanced functions and two applications",

abstract = "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.",

keywords = "Constant composition code, Cyclotomy, Difference system of sets, Generalized cyclotomy, Zero-difference balanced function",

author = "Junying Liu and Yupeng Jiang and Qunxiong Zheng and Dongdai Lin",

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AU - Jiang, Yupeng

AU - Zheng, Qunxiong

AU - Lin, Dongdai

PY - 2019/10/1

Y1 - 2019/10/1

N2 - 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.

AB - 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.

KW - Constant composition code

KW - Cyclotomy

KW - Difference system of sets

KW - Generalized cyclotomy

KW - Zero-difference balanced function

UR - https://www.scopus.com/pages/publications/85061318251

U2 - 10.1007/s10623-019-00616-x

DO - 10.1007/s10623-019-00616-x

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EP - 2265

JO - Designs, Codes, and Cryptography

JF - Designs, Codes, and Cryptography

IS - 10

ER -

A new construction of zero-difference balanced functions and two applications

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Keywords

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