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arXiv · 2107.04790

On balanced $(Z_{4u}\times Z_{8v},\{4,5\},1)$ difference packings

Hengming Zhao·Rongcun Qin·Dianhua Wu
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Abstract

Let $K$ be a set of positive integers and let $G$ be an additive group. A $(G, K, 1)$ difference packing is a set of subsets of $G$ with sizes from $K$ whose list of differences covers every element of $G$ at most once. It is balanced if the number of blocks of size $k\in K$ does not depend on $k$. In this paper, we determine a balanced $(Z_{4u}\times Z_{8v},{4,5},1)$ difference packing of the largest possible size whenever $uv$ is odd. The corresponding optimal balanced $(4u, 8v,\{4,5\},1)$ optical orthogonal signature pattern codes are also obtained.

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Hengming Zhao, Rongcun Qin, Dianhua Wu. 2021-07-10. On balanced $(Z_{4u}\times Z_{8v},\{4,5\},1)$ difference packings. https://arxiv.org/abs/2107.04790

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