### On the Automorphism Groups of the Z2Z4-Linear 1-Perfect and Preparata-Like Codes

**2016-01-29**

1602.00036 | cs.IT

We consider the symmetry group of a $Z_2Z_4$-linear code with parameters of a
$1$-perfect, extended $1$-perfect, or Preparata-like code. We show that,
provided the code length is greater than $16$, this group consists only of
symmetries that preserve the $Z_2Z_4$ structure. We find the orders of the
symmetry groups of the $Z_2Z_4$-linear (extended) $1$-perfect codes. Keywords:
additive codes, $Z_2Z_4$-linear codes, $1$-perfect codes, Preparata-like codes,
automorphism group, symmetry group.

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