New examples of maximal curves with low genus

Abstract

Explicit equations for algebraic curves with genus 4, 5, and 10 that are either maximal or minimal over the finite field with p 2 elements are obtained for infinitely many p's. The key tool is the investigation of their Jacobian decomposition. Lists of small p's for which maximality holds are provided. In some cases we also describe the automorphism group of the curve.