Construction of Hadamard Z₂Z₄Q₈-codes for each allowable value of the rank and dimension of the kernel
This work deals with Hadamard Z₂Z₄Q₈-codes, which are binary codes after a Gray map from a subgroup of a direct product of Z₂, Z₄ and Q₈ groups, where Q₈ is the quaternionic group. In a previous work, these kind of codes were classified in five shapes. In this paper we analyze the allowable range of...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:142691 |
| Acceso en línea: | https://ddd.uab.cat/record/142691 https://dx.doi.org/urn:doi:10.1109/TIT.2015.2398869 |
| Access Level: | acceso abierto |
| Palabra clave: | Combinatorial mathematics Dimension of the kernel Error-correcting codes Hadamard codes Rank Z₂Z₄-codes Z₂Z₄Q₈-codes |
| Sumario: | This work deals with Hadamard Z₂Z₄Q₈-codes, which are binary codes after a Gray map from a subgroup of a direct product of Z₂, Z₄ and Q₈ groups, where Q₈ is the quaternionic group. In a previous work, these kind of codes were classified in five shapes. In this paper we analyze the allowable range of values for the rank and dimension of the kernel, which depends on the particular shape of the code. We show that all these codes can be represented in a standard form, from a set of generators, which help to understand the characteristics of each shape. The main results we present are the characterization of Hadamard Z₂Z₄Q₈-codes as a quotient of a semidirect product of Z₂Z₄-linear codes and, on the other hand, the construction of Hadamard Z₂Z₄Q₈-codes with each allowable pair of values for the rank and dimension of the kernel. |
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