In this article we construct for any prime power q and odd n⩾ 5, a new F q 2 n‐maximal
curve X n. Like the Garcia–Güneri–Stichtenoth maximal curves, our curves generalize the …

Let X be a (projective, geometrically irreducible, non-singular) algebraic curve of genus g≥
2 defined over an algebraically closed field K of odd characteristic p. Let Aut (X) be the …

We construct examples of curves defined over the finite field F q 6 which are covered by the
GK-curve. Thus such curves are maximal over F q 6 although they cannot be covered by the …

Abstract The Giulietti-Korchmáros (GK) function field is the first example of a maximal
function field which is not a subfield of the Hermitian function field over the same constant …

We investigate two families S˜ q and R˜ q of maximal curves over finite fields recently
constructed by Skabelund as cyclic covers of the Suzuki and Ree curves. We show that S˜ q …

For every q= n 3 with na prime power greater than 2, the GK-curve is an F q 2-maximal curve
that is not F q 2-covered by the Hermitian curve. In this paper some Galois subcovers of the …

We investigate the genera of quotient curves ℋ q∕ G of the 𝔽 q 2-maximal Hermitian curve
ℋ q, where G is contained in the maximal subgroup ℳ q≤ A ut (ℋ q) fixing a pole-polar pair …

Let r≥ 3 be an odd integer and F q 2 r the finite field with q 2 r elements. A second
generalisation of the Giulietti-Korchmáros maximal curve over F q 6 was presented in 2018 …

A complete characterization of Galois subfields of the generalized Giulietti–Korchmáros function
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In this paper, we deal with the problem of classifying the genera of quotient curves H _q/GH
q/G, where H _q H q is the F _ q^ 2 F q 2-maximal Hermitian curve and G is an …