Isomorphism classes of hyperelliptic curves of genus 3 over finite fields

Authors:
Yingpu Deng
Affiliations:
Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China
Venue:
Finite Fields and Their Applications
Year:
2006

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Abstract

In this paper we present a direct method to compute the number of isomorphism classes of hyperelliptic curves of genus 3 over finite fields F"q. The number of isomorphism classes is a polynomial in q of degree 5. In all the cases we show an explicit formula for this polynomial. These results can be used in the classification problems and the hyperelliptic curve cryptosystems.