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. In particular some central algorithmic questions of coding theory, both in the Shannon sense and in the Hamming sense are open today, and theoretical computer scientists can (and are) contributing. Readers seeking further material are encouraged to check out the website of the author [90]. More stable sources of information include the classical text of MacWilliams and Sloane [1981], the concise text of van Lint on algebraic coding theory [1999], the out-of-print, but highly recommended, book by Blahut [1983] which is an excellent source for some of the algorithmic works, and the highly detailed (and not-so-handy) handbook of coding theory.