English abstract
Error correcting codes are very useful in sending information over long distances or through channels where errors might occur in the messages. In this project, we will give the basic concept of coding theory and introduce the essential facts and definitions, which are used in this field such as coding, decoding, Hamming distance and Hamming weight.
The emphasis in this project will be on linear codes. Reed-Muller codes are then discussed extensively as an important class of linear codes. Examples will be provided to illustrate the effectiveness of these codes. In addition, a Reed-Muller decoding technique is explained and an example is given to clarify this method. Finally, a brief description of some selected recent results on Reed-Muller codes will be presented.
