ML p(r)ior | On the Automorphism Groups of the Z2Z4-Linear 1-Perfect and Preparata-Like Codes

### 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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