ABSTRACT
This chapter describes linear codes from a geometric point of view. It makes sense, intuitively, to view the 1-dimensional subspaces of V as points and the 2-dimensional subspaces as lines. The main reason is the following: any two points are on precisely one common line. This is clear and it is a familiar axiom in geometry. When describing codes geometrically, the appropriate notion of equivalence of codes is monomial equivalence. When describing codes geometrically, the appropriate notion of equivalence of codes is monomial equivalence. It is the charm of the geometric description of linear codes that it gives a completely different angle under which to view the construction problem. Reconsider Reed-Solomon codes from a geometric point of view. As generator matrices we used Vandermonde matrices.
