A survey of methods for constructing nonlinear perfect binary codes

The theory of perfect codes is an area at the juncture of coding theory and design theory which is rather hard to explore. Linear perfect codes were constructed by M. Golay and R. Hamming in the end of the 1940s. Nonlinear perfect codes were discovered by Yu. L. Vasil'ev in 1961. At present, many different methods are known for constructing perfect codes. This article presents a survey of the methods for constructing nonlinear perfect binary codes alongside some open questions of the theory of perfect codes.