On construction of curves over finite fields with many rational points
finite field | Algebraic curve | rational points | Kummer extension
In this work we give a method to construct algebraic curves over the finite field $F_q$. For many of these curves the number of rational points is close to the best existing upper bounds (records). The method consists in constructing a rational function $u(x)$ associated to two polynomials with coefficents in $F_q$ such that $u(x)$ takes the value 1 for many elements of the finite field $F_q$. Lots of the records that we match here were obtained by totally different methods, so here we have an unified way to get them.