On the dimension of Goppa codes (Q1205124)
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scientific article; zbMATH DE number 146883
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the dimension of Goppa codes |
scientific article; zbMATH DE number 146883 |
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On the dimension of Goppa codes (English)
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1 April 1993
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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.
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dimension codes
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algebraic geometry codes
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lower bound
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divisor
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Riemannian-Roch theorem
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Carlitz-Uchiyama bound
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