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(N\ln N)^2^\vphantom)). [ABSTRACT FROM PUBLISHER]