Constructions Of The Binary Golay Codes

The binary Golay code is a unique nontrivial error-correcting complete code.Therefore, giving the methods of constructing the binary Golay code has important theoretical meanings and practical meanings by analyzing the characteristics of the binary Golay code and using the relevant knowledge of the codes.Firstly, we review some relevant definitions and properties of the codes.Then we discuss basic properties of the binary Golay code.Next,we sum up the methods of constructing the binary Golay code from the Hamming code,the Paley matrix, the QR code, the Hexacode code and the lexicographically least binary code.Finally, we proved that the binary Golay code can be constructed from a S(5,8,24) Steiner system,and that constructing the (24,12,8) binary Golay code is equivalent to constructing a S(5,8,24) Steiner system.