1 Data of the visit

In many situations, it is necessary to transmit data from one place to an other. A classical example is the transmission of data via satellites. Also playing music on a compact disc is an example of data transmission; the music stored in a binary form on the compact disc is transmitted via a laser beam to the compact disc player and reconverted into music. During the transmission of data, it is possible that there occur errors. Atmospheric circumstances can change data in satellite communication; scratches and finger prints on a compact disc can make the binary information stored on the disc unreadable. The crucial question is how these inevitable errors can be corrected. The solution is to construct codes. For practical purposes, we can restrict ourselves to linear codes. Linear codes are described by their four parameters: we speak of [n, k, d; q]-codes. These are k-dimensional subspaces of the n-dimensional vector space V (n, q) over the finite field GF (q), such that two distinct vectors of these subspaces differ in at least d positions. For fixed value of q, the order of the underlying field, the best linear codes are codes with: (1) short length n, for fast data transmission, (2) large dimension k, for a large variety of information that can be transmitted , (3) large minimal distance d, for being able to correct a lot of errors.