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- W2980492531 abstract "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." @default.
- W2980492531 created "2019-10-25" @default.
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- W2980492531 date "2019-10-16" @default.
- W2980492531 modified "2023-09-27" @default.
- W2980492531 title "On the Kernel of $Z_{2^s}$-Linear Simplex and MacDonald Codes" @default.
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