On hadamard full propelinear codes with associated group C2t × C2
We introduce the Hadamard full propelinear codes that factorize as direct product of groups such that their associated group is C2t × C2. We study the rank, the dimension of the kernel, and the structure of these codes. For several specific parameters we establish some links from circulant Hada-mard...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:307004 |
| Acceso en línea: | https://ddd.uab.cat/record/307004 https://dx.doi.org/urn:doi:10.3934/amc.2020041 |
| Access Level: | acceso abierto |
| Palabra clave: | Hadamard full propelinear codes Hadamard matrices Kernel Rank |
| Sumario: | We introduce the Hadamard full propelinear codes that factorize as direct product of groups such that their associated group is C2t × C2. We study the rank, the dimension of the kernel, and the structure of these codes. For several specific parameters we establish some links from circulant Hada-mard matrices and the nonexistence of the codes we study. We prove that the dimension of the kernel of these codes is bounded by 3 if the code is nonlinear. We also get an equivalence between circulant complex Hadamard matrix and a type of Hadamard full propelinear code, and we find a new example of circulant complex Hadamard matrix of order 16. |
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