On Certain Subcovers of the Hermitian Curve

On additive polynomials and certain maximal curves

“…In [1] they are classified under the assumption m = q + 1 and a hypothesis on Weierstrass nongaps at a point; in [4] it is shown that if A(X) has coefficients in the finite field F q and F(Y) = Y q+1 , then the curve C is covered by the Hermitian curve ; and in [5] it is shown that if deg F(Y) = m = q + 1, then the maximality of the curve C implies that the polynomial A(X) has all roots in F q 2 .…”

Quotient curves of the GK curve

“…Proof. Let g H = ℓ(ℓ−1)/2 be the genus of H, and let gL be the genus of the quotient curve H/ L. Then by straightforward computation (14) (…”

“…6], any F q 2 -rational curve which is F q 2 -covered by an F q 2 -maximal curve is also F q 2 -maximal. This has made it possible to obtain several genera of F q 2 -maximal curves by applying the Riemann-Hurwitz formula, especially from the Hermitian curve, see [2,3,1,4,7,8,14,15,20,18,21,22]. Others have been obtained from the DLS and DLR curves, see [24,5,6,28].…”