New partial geometric difference sets and partial geometric difference families |
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Authors: | Jerod Michel |
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Institution: | School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, P. R. China |
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Abstract: | 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. |
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Keywords: | Partial geometric design cyclotomic class directed strongly regular graph partial geometric difference set partial geometric difference family |
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