  The purpose of the present article is the study of duals of functional codes
on algebraic surfaces. We give a direct geometrical description of them, using
differentials. Even if this geometrical description is less trivial, it can be
regarded as a natural extension to surfaces of the result asserting that the
dual of a functional code on a curve is a differential code. We study the
parameters of such codes and state a lower bound for their minimum distance.
Using this bound, one can study some examples of codes on surfaces, and in
particular surfaces with Picard number 1 like elliptic quadrics or some
particular cubic surfaces. The parameters of some of the studied codes reach
those of the best known codes up to now.
