Codes on Drinfeld Curves

Abstract

Considering codes on reductions of classical modular curves we obtain codes over \({\mathbb{F}_{{p^2}}}\) with good asymptoticp properties. To obtain codes with similar properties over \({\mathbb{F}_{{p^2}}}\), q being an arbitrary power of a prime p, one has q to consider Drinfeld modular curves. The latter have a number of advantages as compared with the classical modular curves; they are in many aspects simpler. Unfortunately this does not regard all the aspects of the theory of modular curves. In some cases classical modular curves are more convenient since they come from characteristic zero, which gives a number of essential results unknown for Drinfeld modular curves (e.g. a characterization of their Weierstrass points).