Constructions of two-dimensional optical orthogonal codes of weight three
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910029088555008 |
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| author | Shan, Xiuling Wang, Lidong Chang, Yanxun Wang, Xiaomiao |
| author_facet | Shan, Xiuling Wang, Lidong Chang, Yanxun Wang, Xiaomiao |
| contents | 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 $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_18864 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Constructions of two-dimensional optical orthogonal codes of weight three Shan, Xiuling Wang, Lidong Chang, Yanxun Wang, Xiaomiao Combinatorics 05B05 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 $n$. |
| title | Constructions of two-dimensional optical orthogonal codes of weight three |
| topic | Combinatorics 05B05 |
| url | https://arxiv.org/abs/2602.18864 |