The survey is devoted to perfect codes and related topics. Since earlier there were written several surveys concerning perfect codes (mainly in English), see the list of references, we highlight in more details some results on perfect codes obtained during last years that were not included in the previous surveys. In this paper we only quickly concern the main problems of the perfect codes theory: construction methods, description of properties, lower bounds on such codes, relationships of the perfect codes theory with other mathematical disciplines and in more detailes we discuss the investigation of nontrivial properties of perfect codes. The present state of the manuscript is by far not complete, it highlights mainly the results obtained in the last years in the laboratory “Perfect combinatorial structures” of Sobolev Institute of Mathematics Siberian Branch of Russian Academy of Science. The material presented here reveals the author’s taste and inclinations.

perfect codes, transitive codes, propelinear codes, partitions of the space into perfect codes, intersection of perfect codes, perfect colorings

Mathematical problems and theory of numerical methods