Constructions of algebraic-geometry codes

Based on curves over finite fields with many rational points, we present two constructions of linear codes from local expansions of functions at a fixed rational point. It turns out that codes from our constructions have the same bound on their parameters as Goppa´s (1981) geometry codes. Furthermore, we prove that our second construction is equivalent to Goppa´s construction. Finally, an additional construction of linear codes from maximal curves shows that these codes have better parameters than Goppa´s geometry codes from maximal curves for a certain interval of parameters