Construction of Perfect $q$-ary Codes by Switchings of Simple Components

We suggest a construction of perfect $q$-ary codes by sequential switchings of specialtype components (called simple components) of the Hamming code. We prove that such components are minimal. The construction yields a lower bound on the number of different $q$-ary codes; this is presently the best known bound. We show that this bound cannot be substantially improved using switchings of components of this type.