The classification of orthogonal arrays OA(2048,14,2,7) and some completely regular codes
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916284394897408 |
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| author | Krotov, Denis S. |
| author_facet | Krotov, Denis S. |
| contents | We describe the classification of orthogonal arrays OA$(2048,14,2,7)$, or, equivalently, completely regular $\{14;2\}$-codes in the $14$-cube ($30848$ equivalence classes). In particular, we find that there is exactly one almost-OA$(2048,14,2,7{+}1)$, up to equivalence. As derived objects, OA$(1024,13,2,6)$ ($202917$ classes) and completely regular $\{12,2;2,12\}$- and $\{14, 12, 2; 2, 12, 14\}$-codes in the $13$- and $14$-cubes, respectively, are also classified.
Keywords: binary orthogonal array, completely regular code, binary 1-perfect code. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_05428 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The classification of orthogonal arrays OA(2048,14,2,7) and some completely regular codes Krotov, Denis S. Combinatorics Discrete Mathematics 05B15, 94B25 We describe the classification of orthogonal arrays OA$(2048,14,2,7)$, or, equivalently, completely regular $\{14;2\}$-codes in the $14$-cube ($30848$ equivalence classes). In particular, we find that there is exactly one almost-OA$(2048,14,2,7{+}1)$, up to equivalence. As derived objects, OA$(1024,13,2,6)$ ($202917$ classes) and completely regular $\{12,2;2,12\}$- and $\{14, 12, 2; 2, 12, 14\}$-codes in the $13$- and $14$-cubes, respectively, are also classified. Keywords: binary orthogonal array, completely regular code, binary 1-perfect code. |
| title | The classification of orthogonal arrays OA(2048,14,2,7) and some completely regular codes |
| topic | Combinatorics Discrete Mathematics 05B15, 94B25 |
| url | https://arxiv.org/abs/2311.05428 |