“…This bound gives very good results, and in some cases, the true minimum distance. There are several works that generalize the order bound to get good bounds for the generalized Hamming weights of the AG codes, see for example [3,10,13]. As GH curve is a Castle curve (see [10,Definition 2.4]), then by [10,Proposition 6] and as it was proved in [5,6], we have…”