On automorphisms of generalized algebraic-geometry codes (Q886271)

In coding theory, one often is interested in codes admitting large automorphism group. Certainly, the knowledge of the automorphism group of a code or even of part of this group gives information about the structure of the code and can allow to developing a decoding algorithm. In [IEEE Trans. Inform. Theory 45, No. 7, 2498--2501 (1999; Zbl 0956.94023)] \textit{C. Xing}, \textit{H. Niederreiter} and \textit{K. Y. Lam} introduced a construction of linear codes from algebraic function fields and places of degrees larger than one and called this construction generalized algebraic geometry codes. This kind of codes is a generalization of functional algebraic geometry codes and geometric Goppa codes. In the main part the author constructs automorphisms of generalized algebraic geometry codes from automorphisms of the underlying algebraic function field \(F/\mathbb F_q\). Furthermore, the author shows a connecting between automorphisms of generalized algebraic geometry codes and certain automorphism of the underlying algebraic function field and determines that the automorphism group of a generalized algebraic geometry code is a semidirect product under some hypothesis.