On Z8-linear Hadamard codes
The Z2s -additive codes are subgroups of ZZn2s, and can be seen as a generalization of linear codes over Z2 and Z4. A Zs-linear Hadamard code is a binary Hadamard code which is the Gray map image of a Zs -additive code. It is known that either the rank or the dimension of the kernel can be used to g...
| Autores: | , , |
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| Formato: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:239908 |
| Acesso em linha: | https://ddd.uab.cat/record/239908 https://dx.doi.org/urn:doi:10.1109/TIT.2019.2952599 |
| Access Level: | acceso abierto |
| Palavra-chave: | Rank Kernel Hadamard code Z2s -additive code Gray map Classification |
| Resumo: | The Z2s -additive codes are subgroups of ZZn2s, and can be seen as a generalization of linear codes over Z2 and Z4. A Zs-linear Hadamard code is a binary Hadamard code which is the Gray map image of a Zs -additive code. It is known that either the rank or the dimension of the kernel can be used to give a complete classification for the Z4-linear Hadamard codes. However, when s > 2, the dimension of the kernel of Z2s-linear Hadamard codes of length 2t only provides a complete classification for some values of t and s. In this paper, the rank of these codes is computed for s=3. Moreover, it is proved that this invariant, along with the dimension of the kernel, provides a complete classification, once t ≥ 3 is fixed. In this case, the number of nonequivalent such codes is also established. |
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