Geodesic
Codes on fibre products of Artin–Schreier curves
Diskretnaya Matematika, Tome 13 (2001) no. 2, pp. 3-13 
S. A. Stepanov; M. Kh. Shalalfekh. Codes on fibre products of Artin–Schreier curves. Diskretnaya Matematika, Tome 13 (2001) no. 2, pp. 3-13. http://geodesic.mathdoc.fr/item/DM_2001_13_2_a0/
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     author = {S. A. Stepanov and M. Kh. Shalalfekh},
     title = {Codes on fibre products of {Artin{\textendash}Schreier} curves},
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     url = {http://geodesic.mathdoc.fr/item/DM_2001_13_2_a0/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The purpose of this paper is to construct a new family of smooth projective curves over a finite field $F_q$ with many $F_q$-rational points using fibre products of Artin–Schreier curves. We show that for any curve $X$ in this family the ratio $g(X)/N_q(X)$, where $g(X)$ is the genus and $N_q(X)$ is the number of $F_q$-rational points, is small enough to get geometric Goppa codes with good parameters. This paper extends the results of Stepanov and Özbudak concerning the construction of long codes.

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