Combinatorial lemma and structure of a class of binary codes

A class of complete binary code systems is presented in which one of the symbols of the alphabet is used in any code combination not more than once, in terms of prefix codes of this class and of the operations of inversion and substitution of codes.Translated from Matematicheskie Zametki, Vol. 7, No. 3, pp. 325–331, March, 1970.In conclusion the author expresses his gratitude to G. Pollak who proposed to characterize the factorizations N by a system of calculus with a variable base, and to L. Redei who discussed the problems related to the factorization of finite sets.