Automorphism groups of GRS codes

We look at AG codes associated to P 1, re-examining the problem of determining their automorphism groups (originally investigated by Dür in 1987 using combinatorial techniques) using recent methods from algebraic geometry. We classify those finite groups that can arise as the automorphism group of an AG code and give an explicit description of how these groups appear. We give examples of generalized Reed-Solomon codes with large automorphism groups G, such as G = P SL(2, q), and explicitly describe their G-module structure.