Families of supersingular curves in characteristic 2

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This paper determines the normal forms of hyperelliptic supersingular curves of genus g over an algebraically closed field F of characteristic 2 for 0 < g< 9. We also show that every hyperelliptic supersingular curve of genus 9 over F has an equation y²-y=x¹9+c⁸x⁹+c³x for some c in F₂bar. The paper determines the dimensions of the open locus of hyperelliptic supersingular curves of genus g < 10 over F₂bar.