Counting isomorphism classes of pointed hyperelliptic curves of genus 4 over finite fields with even characteristic
Resource
Acta Mathematica Sinica 26 (6): 1019-1054
Journal
Acta Mathematica Sinica, English Series
Journal Volume
26
Journal Issue
6
Pages
1019-1054
Date Issued
2010
Author(s)
Abstract
This paper is devoted to counting the number of isomorphism classes of pointed hyperelliptic curves over finite fields. We deal with the genus 4 case and the finite fields are of even characteristics. The number of isomorphism classes is computed and the explicit formulae are given. This number can be represented as a polynomial in q of degree 7, where q is the order of the finite field. The result can be used in the classification problems and it is useful for further studies of hyperelliptic curve cryptosystems, e.g. it is of interest for research on implementing the arithmetics of curves of low genus for cryptographic purposes. It could also be of interest for point counting problems; both on moduli spaces of curves, and on finding the maximal number of points that a pointed hyperelliptic curve over a given finite field may have. © 2010 Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg.
Type
journal article
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