The Z2s-additive codes are subgroups of Z2sn, and can be seen as a generalization of linear codes over Z 2 and Z 4 . 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 Z 4 -linear Hadamard codes. In this paper, the kernel of Z2s-linear Hadamard codes of length 2 t 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.
|Number of pages||19|
|Journal||Designs, Codes, and Cryptography|
|Publication status||Published - 15 Mar 2019|
- Gray map
- Hadamard code
- Z2s-additive code
- Z2s-linear code