期刊信息
- 刊名： 河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
- 主办： 河北师范大学
- ISSN： 1000-5854
- CN： 13-1061/N
- 中国科技核心期刊
- 中国期刊方阵入选期刊
- 中国高校优秀科技期刊
- 华北优秀期刊
- 河北省优秀科技期刊
部分几何差族的存在性
- (1.河北师范大学 数学科学学院，河北 石家庄 050024; 2.河北城乡建设学校 基础部，河北 石家庄 050030 )
-
DOI：10.13763/j.cnki.jhebnu.nse.202101020
On the Existence of Partial Geometric Difference Families
摘要/Abstract
摘要：
部分几何差族是组合设计理论中差族概念的推广. 通过对部分几何差族区组结构的分析, 得到了区组长为4且型为（4t, 1, 1）的一类部分几何差族存在的充分必要条件, 并讨论二面体群及阶为2p, 2p², 2pq的非交换群上的这类部分几何差族的存在性问题.
Abstract：
Partial geometric difference family is an extension of difference family in combinatorial design theory. By analyzing the block structures of the partial geometric difference families, we obtain the necessary and sufficient conditions for the existence of a class of partial geometric difference families with block length four and type （4t, 1, 1）. In addition, we discuss the existence of partial geometric difference families on the dihedral group and non-commutative groups with order 2p, 2p² and 2pq.
关键词
Key words：
partial geometric difference family
;
difference family
;
existence
参考文献 6
- [1] KATHLEEN N, OKTAY O, SUNG Y. Partial Geometric Difference Families [J] . J Combin Des, 2016, 24(3):112-131. doi:10. 1002/jcd. 21416
- [2] KATHLEEN N, OKTAY O. Partial Geometric Design with Prescribed Automorphisms [J] . Des Codes Cryptogr, 2016, 80(3):435-451. doi:10. 1007/s10623-015-0111-5
- [3] JEROD M. New Partial Geometric Difference Sets and Partial Geometric Difference Families [J] . Acta Math Sin (Engl Ser), 2017, 33(5):591-606. doi:10. 1007/s10114-016-6151-6
- [4] CHANG Y X, CHENG F Z, ZHOU J L. Partial Geometric Difference Sets and Partial Geometric Difference Families [J] . Discrete Math, 2018, 341(9):2490-2498. doi:10. 1016/j. disc. 2018. 06. 008
- [5] 张迪. 112差族的构造 [D] . 石家庄：河北师范大学, 2018. ZHANG Di. The Constructions of 112difference Families [D] . Shijiazhuang:Hebei Normal University, 2018.
- [6] 吴裕宾. 确定2p, 4p, 2p2, 2pq阶群构造的一种初等方法 [J] . 扬州师院学报(自然科学版), 1989, 9(1):1-9. WU Yubin. A Elementary Method for Determining Construction of Groups of the Order 2p, 4p, 2p2and 2pq [J] . Journal of Yangzhou Teachers College(Natural Science), 1989, 9(1):1-9.