  Perfect codes obtained by the Vasil'ev--Sch\"onheim construction from a
linear base code and quadratic switching functions are transitive and,
moreover, propelinear. This gives at least $\exp(cN^2)$ propelinear $1$-perfect
codes of length $N$ over an arbitrary finite field, while an upper bound on the
number of transitive codes is $\exp(C(N\ln N)^2)$. Keywords: perfect code,
propelinear code, transitive code, automorphism group, Boolean function.
