Classification of the Z2Z4-linear Hadamard codes and their automorphism groups

© 1963-2012 IEEE. A Z2Z4-linear Hadamard code of length α + 2β = 2t is a binary Hadamard code, which is the Gray map image of a Z2Z4-additive code with α binary coordinates and β quaternary coordinates. It is known that there are exactly ⌊t?1 2⌋ and ⌊t2⌋ nonequivalent Z2Z4-linear Hadamard codes of length 2t, with α = 0 and α ≠ 0, respectively, for all t ≥ 3. In this paper, it is shown that each Z2Z4-linear Hadamard code with α = 0 is equivalent to a Z2Z4-linear Hadamard code with α ≠ = 0, so there are only ⌊t2⌋ nonequivalent Z2Z4-linear Hadamard codes of length 2t. Moreover, the order of the monomial automorphism group for the Z2Z4-additive Hadamard codes and the permutation automorphism group of the corresponding Z2Z4-linear Hadamard codes are given.