On the Kernel of \mathbb Z_2^s -Linear Hadamard Codes
نویسندگان
چکیده
The Z2s -additive codes are subgroups of Z n 2s , and can be seen as a generalization of linear codes over Z2 and Z4. A Z2s -linear Hadamard code is a binary Hadamard code which is the Gray map image of a Z2s additive code. It is known that the dimension of the kernel can be used to give a complete classification of the Z4-linear Hadamard codes. In this paper, the kernel of Z2s -linear Hadamard codes and its dimension are established for s > 2. Moreover, we prove that this invariant only provides a complete classification for some values of t and s. The exact amount of nonequivalent such codes are given up to t = 11 for any s ≥ 2, by using also the rank and, in some cases, further computations.
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