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We construct examples of curves defined over the finite field Fq6 which are covered by the GK-curve. Thus such curves are maximal over Fq6 although they cannot be covered by the Hermitian curve for q > 2. We also give examples of maximal curves that cannot be Galois covered by the Hermitian curve over the finite field Fq2n with n > 3 odd and q > 2. We point… (More)
We show that a maximal curve over Fq2 defined by the affine equation y = f(x), where f(x) ∈ Fq2 [x] has degree coprime to n, is such that n is a divisor of q+1 if and only if f(x) has a root in Fq2 . In this case, all the roots of f(x) belong to Fq2 ; cf. Thm. 1.2, Thm. 4.3 in [J. Pure Appl. Algebra 212 (2008), 2513–2521]. In particular, we characterize… (More)
We characterize certain maximal curves over finite fields whose plane models are of Hurwitz type, namely xy +y +x = 0. We also consider maximal hyperelliptic curves of maximal genus. Finally, we discuss maximal curves of type y + y = x via Class Field Theory.