Utilize este identificador para referenciar este registo:
http://hdl.handle.net/10773/36187
Título: | Nonlinearity and kernel of Z2s-linear simplex and MacDonald codes |
Autor: | Fernández-Córdoba, Cristina Vela, Carlos Villanueva, Mercè |
Palavras-chave: | Z2s-linear codes Gray map Simplex codes MacDonald codes Hadamard codes Cosets |
Data: | Nov-2022 |
Editora: | IEEE |
Resumo: | Z2s-additive codes are subgroups of Z2s^n , and can be seen as a generalization of linear codes over Z2 and Z4. A Z2s -linear code is a binary code (not necessarily linear) which is the Gray map image of a Z2s -additive code. We consider Z2s-additive simplex codes of type alpha and beta, which are a generalization over Z2s of the binary simplex codes. These codes are related to the Z2s-additive Hadamard codes. In this paper, we use this relationship to find a linear subcode of the corresponding Z2s-linear codes, called kernel, and a representation of these codes as cosets of this kernel. In particular, this also gives the linearity of these codes. Similarly, Z2s-additive MacDonald codes are defined for s > 2, and equivalent results are obtained. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/36187 |
DOI: | 10.1109/TIT.2022.3172884 |
ISSN: | 0018-9448 |
Aparece nas coleções: | DMat - Artigos |
Ficheiros deste registo:
Ficheiro | Descrição | Tamanho | Formato | |
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23-SimplexMCDonaldPaper.pdf | 347.29 kB | Adobe PDF |
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