Goppa and related codes invariant under a prescribed permutation

We explain how to construct Goppa codes, expurgated or extruded Goppa codes invariant under a permutation induced by an element of the projective semilinear group PΓL(2, GF (p^m)). This follows from the knowledge of semilinear automorphism groups of generalized Reed-Solomon codes. We obtain very good codes: some of them have parameters which reach the values given in the Brouwer table (see Handbook of Coding Theory, V.S. Pless and W.C. Huffman, Eds. Amsterdam, The Netherlands: Elsevier, vol.1, ch.4., 1998).. Moreover, it is easy to construct quasi-cyclic Goppa or related codes. Often, we obtain parameters unknown for quasi-cyclic codes