A family of maximal hyperelliptic curves

Maximal hyperelliptic curves of genus three

Article history: Received 24 June 2008 Revised 29 January 2009 Available online 27 February 2009 Communicated by H. Stichtenoth This note contains general remarks concerning finite fields over which a so-called maximal, hyperelliptic curve of genus 3 exists. Moreover, the geometry of some specific hyperelliptic curves of genus 3 arising as quotients of Fermat curves, is studied. In particular, ...

A note on superspecial and maximal curves

In this note we review a simple criterion, due to Ekedahl, for superspecial curves defined over finite fields.Using this we generalize and give some simple proofs for some well-known superspecial curves.

Arithmetic of Hyperelliptic Curves

A new family of maximal curves over a finite field

A new family of Fq2-maximal curves is presented and some of their properties are investigated.

Families of Hyperelliptic Curves

Throughout this work we deal with a natural number g ≥ 2 and with an algebraically closed field k whose characteristic differs from 2. A hyperelliptic curve of genus g over k is a smooth curve of genus g, that is a double cover of the projective line P. The Riemann-Hurwitz formula implies that this covering should be ramified at 2g + 2 points. Because of this explicit description, hyperelliptic...