On the Kernel of Z_(2~s)-Linear Hadamard Codes

摘要

The Z_(2~s)-additive codes are subgroups of Z_(2~s)~n, and can be seen as a generalization of linear codes over Z_2 and Z_4. A Z_(2~s)-linear Hadamard code is a binary Hadamard code which is the Gray map image of a Z_(2~s)-additive code. For s = 2, the kernel of Z_4-linear Hadamard codes can be used for their complete classification. In this paper, the kernel of Z_(2~s)-linear Hadamard codes is given for s > 2. However, unlike for s = 2, we show that the dimension of the kernel just allows a partial classification of these Hadamard codes.