Counting isomorphism classes of pointed hyperelliptic curves of genus 4 over finite fields with odd characteristic

Abstract: This paper is devoted to computing 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 odd characteristic. The number of isomorphism classes is computed. This number can be represented as a polynomial in of degree 7, where is the order of the finite field. The results have applications in the classification problems and in the hyperelliptic curve cryptosystems. [Copyright &y& Elsevier]