Pure gaps on curves with many rational places

Abstract

We consider the algebraic curve defined by ym=f(x) where m≥2 and f(x) is a rational function over Fq. We extend the concept of pure gap to c-gap and obtain a criterion to decide when an s-tuple is a c-gap at s rational places on the curve. As an application, we obtain many families of pure gaps at two rational places on curves with many rational places.