Generalized Algebraic Geometric Codes From Maximal Curves

Some new results on Generalized Algebraic Geometric (GAG) codes are obtained. First, we provide some constructions which significantly improve the general lower bounds on the minimum distance of a GAG code. GAG codes associated to specific maximal curves over finite fields are then investigated. As a result, 2895 improvements on MinT´s tables are obtained. Finally, we construct asymptotically good GAG codes with better parameters with respect to those constructed by Spera in 2005. Maximal curves play a role in this context as well.