Author:
Zhao Hengming,Qin Rongcun,Wu Dianhua
Abstract
<p style='text-indent:20px;'>Let <inline-formula><tex-math id="M1">\begin{document}$ m $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M2">\begin{document}$ n $\end{document}</tex-math></inline-formula> be positive integers, and <inline-formula><tex-math id="M3">\begin{document}$ K $\end{document}</tex-math></inline-formula> a set of positive integers with size greater than 2. An <inline-formula><tex-math id="M4">\begin{document}$ (m,n,K,1) $\end{document}</tex-math></inline-formula> optical orthogonal signature pattern code, <inline-formula><tex-math id="M5">\begin{document}$ (m,n,K,1) $\end{document}</tex-math></inline-formula>-OOSPC, was introduced by Kwong and Yang for 2-D image transmission in multicore-fiber optical code-division multiple-access (OCDMA) networks with multiple quality of services (QoS) requirement. Let <inline-formula><tex-math id="M6">\begin{document}$ G $\end{document}</tex-math></inline-formula> be an additive group, a balanced <inline-formula><tex-math id="M7">\begin{document}$ (G, K, 1) $\end{document}</tex-math></inline-formula> difference packing, <inline-formula><tex-math id="M8">\begin{document}$ (G, K, 1) $\end{document}</tex-math></inline-formula>-BDP, can be used to construct a balanced <inline-formula><tex-math id="M9">\begin{document}$ (m,n,K,1) $\end{document}</tex-math></inline-formula>-OOSPC when <inline-formula><tex-math id="M10">\begin{document}$ G = {\mathbb{Z}}_m\times {\mathbb{Z}}_n $\end{document}</tex-math></inline-formula>. In this paper, the existences of optimal <inline-formula><tex-math id="M11">\begin{document}$ ( {\mathbb{Z}}_{2u}\times {\mathbb{Z}}_{38v}, \{3,4,5\},1) $\end{document}</tex-math></inline-formula>-BDPs are completely solved with <inline-formula><tex-math id="M12">\begin{document}$ u, \ v\equiv 1\pmod2 $\end{document}</tex-math></inline-formula>, and the corresponding optimal balanced <inline-formula><tex-math id="M13">\begin{document}$ (2u, 38v,\{3,4,5\},1) $\end{document}</tex-math></inline-formula>-OOSPCs are also obtained.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Computer Networks and Communications,Algebra and Number Theory,Applied Mathematics,Discrete Mathematics and Combinatorics,Computer Networks and Communications,Algebra and Number Theory