New partial geometric difference sets and partial geometric difference families
New partial geometric difference sets and partial geometric difference families
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DOI：
10.1007/s10114-016-6151-6
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发表时间：
2015-12
期刊：
影响因子：
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通讯作者：
Jerod Michel
中科院分区：
文献类型：
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作者：
Jerod Michel
利用伽罗瓦环和伽罗瓦域，我们构造了几个无限类的部分几何差集，部分几何差族，与新的参数。此外，这些部分几何差集（和部分几何差族）对应于新的有向强正则图无限族。我们还讨论了部分平衡设计、2-a设计（最近由丁存生在“Codes from Difference Sets”（2015）中提出）和部分几何设计之间的一些联系，并研究了2-a设计何时是部分几何设计。
Using Galois rings and Galois fields, we construct several infinite classes of partial geometric difference sets, and partial geometric difference families, with new parameters. Furthermore, these partial geometric difference sets (and partial geometric difference families) correspond to new infinite families of directed strongly regular graphs. We also discuss some of the links between partially balanced designs, 2-adesigns (which were recently coined by Cunsheng Ding in “Codes from Difference Sets” (2015)), and partial geometric designs, and make an investigation into when a 2-adesign is a partial geometric design.