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arXiv · 2602.18864

Constructions of two-dimensional optical orthogonal codes of weight three

Xiuling Shan·Lidong Wang·Yanxun Chang·Xiaomiao Wang
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Abstract

The study of optical orthogonal codes has been motivated by an application in an optical code-division multiple access system. This paper focuses on optimal two-dimensional optical orthogonal codes with autocorrelation and cross-correlation both equal to $1$. By examining the structures of $n$-cyclic group divisible packings and semi-cyclic incomplete holey group divisible designs, we present new combinatorial constructions for two-dimensional $(m\times n,k,1)$-optical orthogonal codes. As a consequence, the exact number of codewords of an optimal two-dimensional $(m\times n,3,1)$-optical orthogonal code is determined for any positive integers $m$ and $n$.

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Xiuling Shan, Lidong Wang, Yanxun Chang, Xiaomiao Wang. 2026-02-21. Constructions of two-dimensional optical orthogonal codes of weight three. https://arxiv.org/abs/2602.18864

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