In this paper we classify hyperelliptic curves of genus 3 defined over a finite field k of even characteristic. We consider rational models representing all k-isomorphy classes of curves with a given arithmetic structure for the ramification divisor and we find necessary and sufficient conditions for two models of the same type to be k-isomorphic. Also, we compute the automorphism group of each curve and an explicit formula for the total number of curves. © 2003 Elsevier Inc. All rights reserved.
|Journal||Finite Fields and Their Applications|
|Publication status||Published - 1 Jan 2004|
- Automorphism group
- Hyperelliptic curves
- Moduli spaces