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Equivalences among Z 2 s -linear Hadamard codes

2019; Elsevier BV; Volume: 343; Issue: 3 Linguagem: Inglês

10.1016/j.disc.2019.111721

1872-681X

Cristina Fernández-Córdoba, Carlos Vela, Mercè Villanueva,

Advanced Wireless Communication Techniques

The Z2s-additive codes are subgroups of Z2sn, 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. A partial classification of these codes by using the dimension of the kernel is known. In this paper, we establish that some Z2s-linear Hadamard codes of length 2t are equivalent, once t is fixed. This allows us to improve the known upper bounds for the number of such nonequivalent codes. Moreover, up to t=11, this new upper bound coincides with a known lower bound (based on the rank and dimension of the kernel). Finally, when we focus on s∈{2,3}, the full classification of the Z2s-linear Hadamard codes of length 2t is established by giving the exact number of such codes.