On perfect binary codes Original Research Article

Some results on perfect codes obtained during the last 6 years are discussed. The main methods to construct perfect codes such as the method of image-components and the concatenation approach and their implementations to solve some important problems are analyzed. The solution of the ranks and kernels problem, the lower and upper bounds of the automorphism group order of a perfect code, spectral properties, diameter perfect codes, isometries of perfect codes and codes close to them by close-packed properties are considered.