Goppa codes and Tschirnhausen modules

We review the use of rank-2 vector bundles in error-correcting coding theory, introduce the issue of maximal subbundles in this context and give an explicit example of rank-2 bundles naturally associated to an elliptic subcover of the Klein curve. We also describe how codes on curves (and therefore certain associated rank-2 bundles and their maximal subbundles) can be formulated in terms of adeles.