Hermitian codes with automorphism group isomorphic to PGL(2,q) with q odd

Hermitian functional and differential codes defined over divisors with strong combinatorial and algebraic properties have often good performance. Here, those arising from the 2-transitive orbit of PGL(2,q) on the Hermitian curve are investigated. In several cases, such codes have better minimum distance compared with the Goppa lower bound. Results on their automorphism groups are also given.