On the dimension of Goppa codes
The author considers subfield subcodes of algebraic geometry codes. \textit{M. Wirtz} [IEEE Trans. Inform. Theory IT-34, Part II, 1341-1343 (1989; Zbl 0665.94013)] has given a lower bound on the dimension of such codes. In the present paper it is proved that this bound is exact for a sufficiently small divisor. In the proof, the Riemann-Roch theorem and a generalization of the Carlitz-Uchiyama bound due to \textit{G. Lachaud} [J. Number Theory 39, No. 1, 18-40 (1991; Zbl 0741.11048)] play an important role.
scientific article; zbMATH DE number 146883