ISOMORPHISM CLASSES OF HYPERELLIPTIC CURVES OF GENUS 2 OVER F_2n

L. H. Encinas, A. J. Menezes, and J. M. Masque in [2] proposed a classification of isomorphism classes of hyperelliptic curve of genus 2 over finite fields with characteristic different from 2 and 5. Y. Choie and D. Yun in [1] obtained for the number of isomorphic classes of hyperelliptic curves of genus 2 over $F_q$ using direct counting method. In this paper we will classify the isomorphism classes of hyperelliptic curves of genus 2 over $F_{2^n}$ for odd n, represented by an equation of the form $y^2+a_5y=x^5+a_8x+a_{10}(a_5{\neq}0)$.