Geodesic
Codes on fibre products of Artin--Schreier curves
Diskretnaya Matematika, Tome 13 (2001) no. 2, pp. 3-13

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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. 
@article{DM_2001_13_2_a0,
     author = {S. A. Stepanov and M. Kh. Shalalfekh},
     title = {Codes on fibre products of {Artin--Schreier} curves},
     journal = {Diskretnaya Matematika},
     pages = {3--13},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2001_13_2_a0/}
}
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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/