Article ID Journal Published Year Pages File Type
4583337 Finite Fields and Their Applications 2008 12 Pages PDF
Abstract

We study a class of curves over finite fields such that the maximal (respectively minimal) curves of this class form a subclass containing the set of maximal (respectively minimal) curves of Coulter (cf. [R.S. Coulter, The number of rational points of a class of Artin–Schreier curves, Finite Fields Appl. 8 (2002) 397–413, Theorem 8.12]) as a proper subset. We determine the exact number of rational points of the curves in the class and we characterize maximal (respectively minimal) curves of the class as subcovers of some suitable curves. In particular we show that Coulter's maximal curves are Galois subcovers of the appropriate Hermitian curves.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory