The punctured dodecacode is unique
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908761301450752 |
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| author | Grassl, Markus Krotov, Denis Sok, Lin Solé, Patrick |
| author_facet | Grassl, Markus Krotov, Denis Sok, Lin Solé, Patrick |
| contents | The punctured dodecacode is an additive $4$-ary code of length $11$ and distance $5$ which is uniformly packed. We show that a code with the same weight distribution is equivalent to it. This code is also shown to be nonlinear.
We also establish the nonexistence of analogues of the dodecacode and the punctured dodecacode in Doob graphs. To that end, we classify two-weight codes of weights $6$ and $8$ in Doob and $4$-ary Hamming graphs of diameter $9$ and the corresponding strongly regular graphs.
Keywords: dodecacode, additive code, trace Hermitian duality, uniformly packed code, completely regular code, Doob graph, strongly regular graph |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08008 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The punctured dodecacode is unique Grassl, Markus Krotov, Denis Sok, Lin Solé, Patrick Combinatorics 05E30, 94B05 The punctured dodecacode is an additive $4$-ary code of length $11$ and distance $5$ which is uniformly packed. We show that a code with the same weight distribution is equivalent to it. This code is also shown to be nonlinear. We also establish the nonexistence of analogues of the dodecacode and the punctured dodecacode in Doob graphs. To that end, we classify two-weight codes of weights $6$ and $8$ in Doob and $4$-ary Hamming graphs of diameter $9$ and the corresponding strongly regular graphs. Keywords: dodecacode, additive code, trace Hermitian duality, uniformly packed code, completely regular code, Doob graph, strongly regular graph |
| title | The punctured dodecacode is unique |
| topic | Combinatorics 05E30, 94B05 |
| url | https://arxiv.org/abs/2601.08008 |