turkmath.org

Coding theory is a field that allows us to construct methods to transfer and store data in a way that can detect and correct corruptions that may occur during the transmission process. Algebraic coding theory uses algebraic structures to construct these methods. Cyclic codes, which are very useful due to their algebraic properties, have a central importance in algebraic coding theory. m-adic residue codes are a type of codes that generates cyclic codes with the help of residue classes. After briefly talking about algebraic coding theory, I will describe cyclic codes and m-adic residue codes. Then, after briefly summarizing the DNA codes, I will explain the relationship between m-adic residue codes and these codes. Finally, I will talk about quantum codes and explain their relationship with m-adic residue codes.