Codes on fibre products of Artin–Schreier curves

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.