Propelinear 1-Perfect Codes From Quadratic Functions
Denis S. Krotov, Vladimir N. Potapov · IEEE Transactions on Information Theory · 2014
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(cN2) 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)).