Note on the genus of certain curves defined on finite fields

摘要

We prove the following results which was conjectured by Stichtenoth and Xing: let g be the genus of a non-singular algebraic curve defined over the finite field F(sub q)(sup 2) and whose number of F(sub q)(sup 2)-rational points attains the Hasse-Weil bound; then either 4g (<=) (q-1)(sup 2) or 2g = (q-1)q. (author). 6 refs. (Atomindex citation 26:064202)