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| 一类新的广义零差分平衡函数及其应用 | |
| 引用本文： | 蒋 林,廖群英. 一类新的广义零差分平衡函数及其应用[J]. 数学年刊A辑(中文版), 2016, 37(3): 243-260 |
| 作者姓名： | 蒋 林 廖群英 |
| 作者单位： | 四川师范大学数学与软件科学学院, 成都 610066.,通讯作者. 四川师范大学数学与软件科学学院, 成都 610066. |
| 基金项目： | 本文受到国家自然科学基金 (No.,11401408)和四川省科技厅科研重点项目 (No.2016JY0134)的资助 |
| 摘 要： | 2008-2009年,丁存生在构造最佳常组合码与优化及完善差分系统中首次引入了零差分平衡(简称ZDB)函数的概念,据此学者们构造出了最佳组成权重码和最优跳频序列.作者将零差分平衡函数的定义推广到一般的广义零差分平衡函数,并利用2分圆陪集构造了一类广义零差分平衡函数,由此构造出一类新的常组合码和差分系统. |
| 关 键 词： | 零差分平衡函数 $2$分圆陪集 常组合码 差分系统 |
| 收稿时间： | 2015-04-14 |
| 修稿时间： | 2015-12-22 |
A New Class of Generalized Zero-Difference Balanced Functions and Applications |
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| JIANG Lin and LIAO Qunying. A New Class of Generalized Zero-Difference Balanced Functions and Applications[J]. Chinese Annals of Mathematics, 2016, 37(3): 243-260 | |
| Authors: | JIANG Lin and LIAO Qunying |
| Affiliation: | Institute of Mathematics and Software Science, Sichuan Normal University,Chengdu 610066, China. and Corresponding author. Institute of Mathematics and Software Science,Sichuan Normal University, Chengdu 610066, China. |
| Abstract: | From 2008 to 2009, zero-difference balanced (ZDB for short) functions were first introducedby Ding in constructing optimal constant composition codes, and optimaland perfect difference systems of sets. Basing on such functions, scholarshave been constructed optimal constant weight codes and optimal frequencyhopping sequences. In this paper, by generalizing the definition of thezero-difference balanced function to the generalized zero-differencebalanced function, some generalized zero differential balance functionsare constructed based on $2$-cyclotomic cosets. Furthermore, a new classof constant composition codes and difference systems of sets are constructed. |
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