ABSTRACT

We have reached a point where we understand the basic notions and objectives of coding theory. The most important family introduced thus far is the Reed-Solomon codes of Chapter 4. The recursive techniques of Chapter 5, in particular concatenation, allow the construction of large classes of codes. This allows the construction of universal hash classes as well (see Chapter 6). Where the classical application of codes for the transmission of messages via noisy channels is concerned, we know the principle of syndrome decoding (Section 3.7) but we do not have a really effective algorithm yet.