On the dimension of Goppa codes
type: Item
instance of: scholarly article
title: On the dimension of Goppa codes
zbMATH Open document ID: 0772.94015
DOI: 10.1007/BF01294836
author: François Rodier
published in: Applicable Algebra in Engineering, Communication and Computing
publication date: 1993-04-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 94B27
zbMATH DE Number: 146883
zbMATH Keywords: dimension codes
zbMATH Keywords: algebraic geometry codes
zbMATH Keywords: lower bound
zbMATH Keywords: divisor
zbMATH Keywords: Riemannian-Roch theorem
zbMATH Keywords: Carlitz-Uchiyama bound
reviewed by: L. M. G. M. Tolhuizen
MaRDI profile type: Publication
cites work: Codes and information
cites work: Artin-Schreier curves, exponential sums, and the Carlitz-Uchiyama bound for geometric codes
cites work: Q4146667
cites work: Exponential sums and Goppa codes. II
cites work: On the parameters of Goppa codes
full work available at URL: https://doi.org/10.1007/bf01294836
OpenAlex ID: W2050042603
description: scientific article; zbMATH DE number 146883