Algebraic Coding Theory

With Jordan Tousignant and Andrew Walker

There are three main reasons to encode data: efficiency, error detection/correction, and secrecy. Encoding for error correction is the subject of coding theory; it is concerned with the reliable transmission of digital messages. In this project we will study various coding methods and their effectiveness, such as check digit schemes and the Hamming code. More importantly, we will see how algebra is used in the process! This will include some modular arithmetic and linear algebra over finite fields. The only prerequisite is Math 31.