Coding Theory: Tutorial & Survey

Coding theory has played a central role in the theoretical computer science. Computer scientists have long exploited notions, constructions, theorems and techniques of coding theory. More recently, theoretical computer science has also been contributing to the theory of error-correcting codes in particular in making progress on some fundamental algorithmic connections. Here we survey some of the central goals of coding theory and the progress made via algebraic methods. We stress that this is a very partial view of coding theory and a lot of promising combinatorial and probabilistic approaches are not covered by this survey.