On the Number of Quadratic Forms Having Codimension 2 Radicals in Characteristic 2 Giving Maximal/Minimal Curves
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Let F-q be an arbitrary finite field of characteristic 2 and k be an arbitrary even integer. We count the number of quadratic forms having codimension 2 radicals on F-q(k) over F-q such that the corresponding curve is maximal or minimal. This problem is first attempted in , in which the number of maximal curves is obtained only for (q, k) = (2, 6) and (q, k) = (2, 8).