Construction and classification of Z2s-linear Hadamard codes
نویسندگان
چکیده
The Z2s-additive and Z2Z4-additive codes are subgroups of Z n 2 and Z α 2 × Z β 4 , respectively. Both families can be seen as generalizations of linear codes over Z2 and Z4. A Z2s-linear (resp. Z2Z4-linear) Hadamard code is a binary Hadamard code which is the Gray map image of a Z2s-additive (resp. Z2Z4-additive) code. It is known that there are exactly ⌊ t−1 2 ⌋ and ⌊ t 2⌋ nonequivalent Z2Z4-linear Hadamard codes of length 2, with α = 0 and α 6= 0, respectively, for all t ≥ 3. In this paper, new Z2s-linear Hadamard codes are constructed for s > 2, which are not equivalent to any Z2Z4-linear Hadamard code. Moreover, for each s > 2, it is claimed that the new constructed nonlinear Z2s-linear Hadamard codes of length 2 t are pairwise nonequivalent.
منابع مشابه
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عنوان ژورنال:
- Electronic Notes in Discrete Mathematics
دوره 54 شماره
صفحات -
تاریخ انتشار 2016