On the Kernel of $\Z_{2^s}$-Linear Simplex and MacDonald Codes
| Autor: | Fernández-Córdoba, Cristina, Vela, Carlos, Villanueva, Mercè |
|---|---|
| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | The $\Z_{2^s}$-additive codes are subgroups of $\Z^n_{2^s}$, and can be seen as a generalization of linear codes over $\Z_2$ and $\Z_4$. A $\Z_{2^s}$-linear code is a binary code which is the Gray map image of a $\Z_{2^s}$-additive code. We consider $\Z_{2^s}$-additive simplex codes of type $\alpha$ and $\beta$, which are a generalization over $\Z_{2^s}$ of the binary simplex codes. These $\Z_{2^s}$-additive simplex codes are related to the $\Z_{2^s}$-additive Hadamard codes. In this paper, we use this relationship to establish the kernel of their binary images, under the Gray map, the $\Z_{2^s}$-linear simplex codes. Similar results can be obtained for the binary Gray map image of $\Z_{2^s}$-additive MacDonald codes. Comment: arXiv admin note: text overlap with arXiv:1801.05189 |
| Databáze: | arXiv |
| Externí odkaz: |
|