  Recently it was proved that if a linear code is invariant under the action of
a doubly transitive permutation group, it achieves the capacity of erasure
channel. Therefore, it is of sufficient interest to classify all codes,
invariant under such permutation groups. We take a step in this direction and
give a review of all suitable groups and the known results on codes invariant
under these groups. It turns out that there are capacity-achieving families of
algebraic geometric codes.
