Unbiased weighing matrices of weight $9$
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916823307386880 |
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| author | Araya, Makoto Harada, Masaaki Kharaghani, Hadi Suda, Sho Yu, Wei-Hsuan |
| author_facet | Araya, Makoto Harada, Masaaki Kharaghani, Hadi Suda, Sho Yu, Wei-Hsuan |
| contents | We investigate unbiased weighing matrices of weight $9$ and provide a construction method using mutually suitable Latin squares. For $n \le 16$, we determine the maximum size among sets of mutually unbiased weighing matrices of order $n$ and weight $9$. Notably, our findings reveal that $13$ is the smallest order where such pairs exist, and $16$ is the first order for which a maximum class of unbiased weighing matrices is found. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15444 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unbiased weighing matrices of weight $9$ Araya, Makoto Harada, Masaaki Kharaghani, Hadi Suda, Sho Yu, Wei-Hsuan Combinatorics 05B20 We investigate unbiased weighing matrices of weight $9$ and provide a construction method using mutually suitable Latin squares. For $n \le 16$, we determine the maximum size among sets of mutually unbiased weighing matrices of order $n$ and weight $9$. Notably, our findings reveal that $13$ is the smallest order where such pairs exist, and $16$ is the first order for which a maximum class of unbiased weighing matrices is found. |
| title | Unbiased weighing matrices of weight $9$ |
| topic | Combinatorics 05B20 |
| url | https://arxiv.org/abs/2501.15444 |