Codes on fibre products of Artin-Schreier curves

Abstract

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