ABSTRACT

This chapter aims to learn how to interpret linear codes geometrically. Starting point is a generator matrix of the code. The difference between triples and points is that triples, which are scalar multiples of each other, define the same point. In this case each point of the Fano plane occurs precisely once as a column. A geometer would identify this code C with the Fano plane itself. A link or bus is a subset of the sites. In order to avoid congestion it is required that every two sites appear together on at least one link. Each site is equipped with a limited number of communication ports and hence can appear on at most some fixed number r of the links. This construction problem for network topologies has been studied extensively. For an introduction, literature and combinatorial-geometric links see Colbourn.