A note on the Assmus--Mattson theorem for some ternary codes (a resume)
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910336319225856 |
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| author | Bannai, Eiichi Miezaki, Tsuyoshi Nakasora, Hiroyuki |
| author_facet | Bannai, Eiichi Miezaki, Tsuyoshi Nakasora, Hiroyuki |
| contents | Let $C$ be a two and three-weight ternary code. Furthermore, we assume that $C_\ell$ are $t$-designs for all $\ell$ by the Assmus--Mattson theorem. We show that $t \leq 5$. As a corollary, we provide a new characterization of the (extended) ternary Golay code. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_08081 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A note on the Assmus--Mattson theorem for some ternary codes (a resume) Bannai, Eiichi Miezaki, Tsuyoshi Nakasora, Hiroyuki Combinatorics Information Theory Primary 05B05, Secondary 94B05, 20B25 Let $C$ be a two and three-weight ternary code. Furthermore, we assume that $C_\ell$ are $t$-designs for all $\ell$ by the Assmus--Mattson theorem. We show that $t \leq 5$. As a corollary, we provide a new characterization of the (extended) ternary Golay code. |
| title | A note on the Assmus--Mattson theorem for some ternary codes (a resume) |
| topic | Combinatorics Information Theory Primary 05B05, Secondary 94B05, 20B25 |
| url | https://arxiv.org/abs/2309.08081 |