On the realization of subgroups of $PGL(2,F)$, and their automorphism groups, as Galois groups over function fields

Let $F$ be any field. We give a short and elementary proof that any finite subgroup $G$ of $PGL(2,F)$ occurs as a Galois group over the function field $F(x)$. We also develop a theory of descent to subfields of $F$. This enables us to realize the automorphism groups of finite subgroups of $PGL(2,F)$ as Galois groups.

Quantum codes from a new construction of self-orthogonal algebraic geometry codes

We present new quantum codes with good parameters which are constructed from self-orthogonal algebraic geometry codes. Our method permits a wide class of curves to be used in the formation of these codes, which greatly extends the class of a previous paper due to Munuera, Tenorio and Torres. These results demonstrate that there is a lot more scope for constructing self-orthogonal AG codes than was previously known.