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 di...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.展开更多
The concept of a （q, k, λ, t） almost dltterence tamlly （ADF） nas oeen introduced and studied by C. Ding and J. Yin as a useful generalization of the concept of an almost difference set. In this paper, we consider...The concept of a （q, k, λ, t） almost dltterence tamlly （ADF） nas oeen introduced and studied by C. Ding and J. Yin as a useful generalization of the concept of an almost difference set. In this paper, we consider, more generally, （q, K,λ, t, Q）-ADFs, where K = {k1, k2,.…, kr} is a set of positive integers and Q = （q1,q2,... ,qr） is a given block-size distribution sequence. A necessary condition for the existence of a （q, K, λ, t, Q）-ADF is given, and several infinite classes of （q, K, A, t, Q）-ADFs are constructed.展开更多
文摘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.
基金Acknowledgements The authors wish to thank the anonymous referees for their helpful comments and suggestions that much improved the quality of this paper. The work of Dianhua Wu was supported in part by the National Natural Science Foundation of China （No. 11271089）, the Guangxi Natural Science Foundation （No. 2012GXNSFAA053001）, the Foundation of Guangxi Education Department （No. 201202ZD012）, and the Guangxi ＇Ba Gui＇ Team for Research and Innovation.
文摘The concept of a （q, k, λ, t） almost dltterence tamlly （ADF） nas oeen introduced and studied by C. Ding and J. Yin as a useful generalization of the concept of an almost difference set. In this paper, we consider, more generally, （q, K,λ, t, Q）-ADFs, where K = {k1, k2,.…, kr} is a set of positive integers and Q = （q1,q2,... ,qr） is a given block-size distribution sequence. A necessary condition for the existence of a （q, K, λ, t, Q）-ADF is given, and several infinite classes of （q, K, A, t, Q）-ADFs are constructed.
