On the Structure of Symmetry Groups of Vasil'ev Codes

The structure of symmetry groups of Vasil'ev codes is studied. It is proved that the symmetry group of an arbitrary perfect binary non-full-rank Vasil'ev code of length $n$ is always nontrivial; for codes of rank $n-\log(n+1)+1$, an attainable upper bound on the order of the symmetry group is obtained.