Balanced ($\mathbb{Z} _{2u}\times \mathbb{Z}_{38v}$, {3, 4, 5}, 1) difference packings and related codes
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Abstract
Let $ m $, $ n $ be positive integers, and $ K $ a set of positive integers with size greater than 2. An $ (m,n,K,1) $ optical orthogonal signature pattern code, $ (m,n,K,1) $-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 $ G $ be an additive group, a balanced $ (G, K, 1) $ difference packing, $ (G, K, 1) $-BDP, can be used to construct a balanced $ (m,n,K,1) $-OOSPC when $ G = {\mathbb{Z}}_m\times {\mathbb{Z}}_n $. In this paper, the existences of optimal $ ( {\mathbb{Z}}_{2u}\times {\mathbb{Z}}_{38v}, \{3,4,5\},1) $-BDPs are completely solved with $ u, \ v\equiv 1\pmod2 $, and the corresponding optimal balanced $ (2u, 38v,\{3,4,5\},1) $-OOSPCs are also obtained.
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Keywords:
- Balanced,
- difference matrix,
- difference packing,
- optical orthogonal signature pattern code,
- semi-cyclic group divisible design.
Mathematics Subject Classification: Primary: 05B40; Secondary: 94C30.Citation: -
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References
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