On the Kernel of _2^s-Linear Simplex and MacDonald Codes
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The _2^s-additive codes are subgroups of ^n_2^s, and can be seen as a generalization of linear codes over _2 and _4. A _2^s-linear code is a binary code which is the Gray map image of a _2^s-additive code. We consider _2^s-additive simplex codes of type α and β, which are a generalization over _2^s of the binary simplex codes. These _2^s-additive simplex codes are related to the _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 _2^s-linear simplex codes. Similar results can be obtained for the binary Gray map image of _2^s-additive MacDonald codes.
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