On the genus spectrum of maximal curves over finite fields

Abstract

In this article, we investigate the genus spectrum of maximal curves. We give the list of genera of all subfields that were found in three main articles, and we exhibit some mistakes that have been done in these articles. Calculations are made for the base fields with cardinality q², where q is a power of 2, 3, 5, 7, 11, 13, 17, 19, 23 and less than 2¹⁴, 3⁹, 5⁶, 7⁵, 11⁴, 13³, 17³, 19³, 23³, respectively.

Keywords:

• Function fields
• genus
• finite fields

AMS Subject Class [2000]:

• Primary 11G20
• Secondary 14G05