Abstract
It is known that extended Goppa cedes are invariant under the group of transformations <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z \rightarrow (A Z + B ) / ( CZ + D )</tex> , with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A D + BC \neq 0</tex> . This invariance is used here to classify cubic and quartic irreducible Goppa codes and to investigate their symmetry groups. A computer has been used to determine the actual group of the codes of length 33 (for cubics and quarries). It has been said, concerning the trends in symmetry groups with respect to the Gilbert bound, that "a good family of codes can be linear or have many symmetries, hut not both" [8]. The groups found here are rather small; and so the results reinforce that statement.
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