The algebraic geometric codes which were introduced by V. D. Goppa in 1977 [7,8]-we call them geometric Goppa codes--can be used to prove the existence of long linear codes which are better than the Gilbert-Varshamov bound. There are many good expositions of this important result [ll, 13, 15, 181. In that context one has to consider curves of high genus which admit many rational points. On the other hand, new interesting codes were found among the geometric Goppa codes by looking at special curves, e.g., elliptic curves, Hermite curves, or Artin-Schreier curves [3-5, 8, 13, 16, 171. In coding theory, one is often interested in codes admitting many automorphisms (e.g., cyclic codes). Goppa [lS] already observed that automorphisms of the underlying algebraic curve induce automorphisms of the associated geometric codes. Since Goppa’s paper is not quite correct we shall give a detailed exposition of this connexion in Section 2. Section 3 is the central part of our paper. It is devoted to the case of geometric Goppa codes associated with a curve of genus 0 (so-called rational Goppa codes). These codes are particularly interesting since many well-known classes of codes (e.g., BCH codes, classical Goppa codes, Reed-Solomon codes, Cauchy codes [6]) can be represented as rational Goppa codes or subfield subcodes of them Cl?]. Our main result is Theorem 3.1. It states that in general all automorphisms of a rational Goppa code are induced by automorphisms of the rational curve, i.e., by projective transformations of the projective line.