ABSTRACT
This chapter focuses on one important area of applications for codes, transmission of messages over noisy channels. It has been mentioned early on in this text that the applications of the concept of codes are manifold and certainly not limited to this historically first area. It is time to take a step in this direction. Applications in cryptography are described in Stinso. To give just one example, when a long document is to be signed electronically one applies at first a hash function to produce a much shorter string and then applies the signature scheme to this hash value. The idea behind universal hashing is to use a carefully chosen family of hash functions instead of a single hash function. Whenever a hash function has to be applied it will be chosen at random from the hash family. The Hamming distance is the number of coordinates where there is no collision.
