On the automorphisms of generalized algebraic geometry codes

We consider the class of generalized algebraic geometry codes (GAG codes) formed by two collections of places, with places of the same degree in each collection. We introduce the concept of N1N2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_1N_2$$\end{document}-automorphism group of a GAG code in this class-that is, a subgroup of the automorphism group of the code. Then we determine a subgroup of the N1N2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_1N_2$$\end{document}-automorphism group in the general case and the N1N2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_1N_2$$\end{document}-automorphism group itself in the rational function field case. We also explicitly construct such a group. This paper presents a method to obtain similar results for the GAG codes that have more collections of places of the same degree in their construction.