Within the scope of this study, the following issues are generally mentioned. First of all, some general information about coding theory is given. Coding types are mentioned and the importance of coding theory in the communication system is mentioned. In the branch of coding theory, various studies have been carried out in order to prevent all distortions that may occur as a result of external factors in the transfer process and storage of the data to be transmitted, especially by creating a connection with different areas of mathematics.

The history of the Golay Codes and the importance of these codes in providing data transmission between the Earth and the spacecraft launched to Saturn and Jupiter within the scope of the Voyager Program are included. Then, the definition of Golay Codes was made and the properties of Binary and Ternary Golay Codes were emphasized. Binary Golay Code was developed as a kind of linear error correction code used in digital communication systems. Then, the definition and characteristics of the Hamming Codes were included and explanations were made with examples. It is aimed to detect and even correct errors by adding additional bits to the data sent against the distortions that may occur during the transmission of the data on the computer.These ideas are given together with the proofs of the basic and important theorems of the Golay and Hamming Codes.In addition, by referring to the definition of Perfect Code, it has been proven that Golay Codes and Hamming Codes are Perfect Codes. These codes give very successful results in the correction of errors that may occur in communication systems.