Generalized AG codes and generalized duality

In (J. Pure Appl. Algebra 55 (1988) 199), Stichtenoth gave sufficient conditions for algebraic–geometric Goppa codes to be self-dual. We adapt this work using differentials to the setting of generalized AG codes introduced by Xing et al. (IEEE Trans. Inform. Theory 45 (1999) 2498). As a consequence we are naturally led to generalized notions of duality for codes. Many examples are presented.