ALGEBRAIC FUNCTION-FIELDS OVER FINITE-FIELDS WITH MANY RATIONAL PLACES

Algebraic function fields (or equivalently, algebraic curves) provide a useful tool for coding theory (for instance, algebraic-geometric cod es and trace codes), but also for other branches of information theory , In these applications, the number of rational places of a function f ield plays a crucial role, One is particularly interested in function fields having a large number of rational places, After a short introdu ction into the mathematical theory of algebraic functions, the paper g ives a survey of old and new results on the number of rational places of function fields.