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29. Balanced ($\mathbb{Z} _{2u}\times \mathbb{Z}_{38v}$, {3, 4, 5}, 1) difference packings and related codes

Author

Hengming Zhao, Rongcun Qin, and Dianhua Wu

Subjects
Algebra and Number Theory, Computer Networks and Communications, Applied Mathematics, Discrete Mathematics and Combinatorics, Microbiology
Abstract

Let \begin{document}$ m $\end{document}, \begin{document}$ n $\end{document} be positive integers, and \begin{document}$ K $\end{document} a set of positive integers with size greater than 2. An \begin{document}$ (m,n,K,1) $\end{document} optical orthogonal signature pattern code, \begin{document}$ (m,n,K,1) $\end{document}-OOSPC, was introduced by Kwong and Yang for 2-D image transmission in multicore-fiber optical code-division multiple-access (OCDMA) networks with multiple quality of services (QoS) requirement. Let \begin{document}$ G $\end{document} be an additive group, a balanced \begin{document}$ (G, K, 1) $\end{document} difference packing, \begin{document}$ (G, K, 1) $\end{document}-BDP, can be used to construct a balanced \begin{document}$ (m,n,K,1) $\end{document}-OOSPC when \begin{document}$ G = {\mathbb{Z}}_m\times {\mathbb{Z}}_n $\end{document}. In this paper, the existences of optimal \begin{document}$ ( {\mathbb{Z}}_{2u}\times {\mathbb{Z}}_{38v}, \{3,4,5\},1) $\end{document}-BDPs are completely solved with \begin{document}$ u, \ v\equiv 1\pmod2 $\end{document}, and the corresponding optimal balanced \begin{document}$ (2u, 38v,\{3,4,5\},1) $\end{document}-OOSPCs are also obtained.

Published
2022

50. 42-Decomposable super-simple (v,4,8)-BIBDs

Author

Jingyuan Chen, Huangsheng Yu, R. Julian R. Abel, and Dianhua Wu

Subjects
Discrete Mathematics and Combinatorics, Theoretical Computer Science
Published
2022

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