Algorithmic Issues in Coding Theory

The goal of this article is to provide a gentle introduction to the basic definitions, goals and constructions in coding theory. In particular we focus on the algorithmic tasks tackled by the theory. We describe some of the classical algebraic constructions of error-correcting codes including the Hamming code, the Hadamard code and the Reed Solomon code. We describe simple proofs of their error-correction properties. We also describe simple and e cient algorithms for decoding these codes. It is our aim that a computer scientist with just a basic knowledge of linear algebra and modern algebra should be able to understand every proof given here. We also describe some recent developments and some salient open problems.