Propelinear 1-Perfect Codes From Quadratic Functions

Perfect codes obtained by the Vasil'ev-Schönheim 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(NlnN)
^2\vphantom)
).