| 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,2016,37(3):243~260 |
| 一类新的广义零差分平衡函数及其应用 |
| A New Class of Generalized Zero-Difference Balanced Functions and Applications |
| Received:April 14, 2015 Revised:December 22, 2015 |
| DOI： |
| 中文关键词: 零差分平衡函数, $2$分圆陪集, 常组合码, 差分系统 |
| 英文关键词: |
| 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 |
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| 中文摘要: |
| 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. |
| 英文摘要: |
| From 2008 to 2009, zero-difference balanced (ZDB for short) functions were first introduced
by Ding in constructing optimal constant composition codes, and optimal
and perfect difference systems of sets. Basing on such functions, scholars
have been constructed optimal constant weight codes and optimal frequency
hopping sequences. In this paper, by generalizing the definition of the
zero-difference balanced function to the generalized zero-difference
balanced function, some generalized zero differential balance functions
are constructed based on $2$-cyclotomic cosets. Furthermore, a new class
of constant composition codes and difference systems of sets are constructed. |
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