集合差系统的新构造
PDF下载 (150)沈淑钰,包经俊*.集合差系统的新构造[J].宁波大学学报(理工版),2024,37(2):78-85.DOI:10.20098/j.cnki.1001-5132.2023.0604
SHEN Shuyu,BAO Jingjun.New constructions of difference systems of sets[J].Journal of Ningbo University(Natural Science & Engineering Edition),2024,37(2):78-85.DOI:10.20098/j.cnki.1001-5132.2023.0604
| Title: | New constructions of difference systems of sets |
| 作者: | 沈淑钰, 包经俊* |
| Author(s): | SHEN Shuyu, BAO Jingjun |
| 关键词: | 集合差系统; 分圆类; 差覆盖; 码字同步 |
| Keywords: | difference system of sets; cyclotomic class; difference covering; code synchronization |
| 分类号: | O157.2 |
| DOI: | 10.20098/j.cnki.1001-5132.2023.0604 |
| 文献标识码: | A |
| 摘要: | 研究集合差系统新的构造方法. 借助有限域上分圆类, 给出集合差系统的两个直接构造; 再利用克罗内克积建立集合差系统新的递归构造, 并推广了已知构造. 最后应用所得到的直接构造和递归构造给出了新的渐近最优的集合差系统 |
| Abstract: | In this paper, we study new constructions of difference systems of sets. Two direct constructions of difference systems of sets are presented using cyclotomic classes over finite fields, and a new recursive construction of difference systems of sets is established using Kronecker product, which can be viewed as a generalization of the known constructions. By applying these direct and recursive constructions, some infinite series of asymptotically optimal difference systems of sets can be constructed. |
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| 备注/Memo: | 收稿日期: 2023−06−12. 宁波大学学报（理工版）网址: http://journallg.nbu.edu.cn/ 基金项目: 国家自然科学基金（11701303）. 第一作者: 沈淑钰, 硕士研究生, 主要研究方向: 组合数学. E-mail: 1162659967@qq.com *通信作者: 包经俊, 博士/副教授, 主要研究方向: 组合数学. E-mail: baojingjun@nbu.edu.cn 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ |
