Abstract
In this paper we study the computation of the number of isomorphism classes of hyperelliptic curves of genus 2 over finite fields Fq with q even. We show the formula of the number of isomorphism classes, that is, for q = 2m, if 4 ∤ m, then the formula is 2q3 + q2 − q; if 4 | m, then the formula is 2q3 + q2 − q + 8. These results can be used in the classification problems and the hyperelliptic curve cryptosystems.
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