Linkage and codes on complete intersections

This note is meant to be an introduction to cohomological methods and their use in the theory of error-correcting codes. In particular we consider evaluation codes on a complete intersection. The dimension of the code is determined by the Koszul complex for X subset of P-2 and a lower bound for the minimal distance is obtained through linkage. By way of example our result fits the well-known formula for the minimal distance of the Generalized Reed-Muller code.