In early 1950's, Richard Hamming established the foundations of the theory of Error-Correcting Codes, which are indispensable for any form of telecommunication (such as internet, cellphone, satellite) or physical data storage (such as hard drive, DVD) nowadays. Our study focused on linear codes, which can be seen as the image of a linear transformation, and on cyclic codes, which are isomorphic to ideals of a ring. Some special linear codes were also studied, such as Reed-Solomon codes.