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On the Automorphism Groups of the Z2Z4-Linear 1-Perfect and Preparata-Like Codes
January 29, 2016 Β· Declared Dead Β· π Designs, Codes and Cryptography
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Authors
Denis Krotov
arXiv ID
1602.00036
Category
cs.IT: Information Theory
Cross-listed
cs.DM,
math.CO
Citations
1
Venue
Designs, Codes and Cryptography
Last Checked
4 months ago
Abstract
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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