Abstract In 1997, Hou and Langevin introduced the idea of constructing bent functions as the composition of a Boolean function with a permutation. Recently, K. Li, C. Li, T. Helleseth, and L. Qu constructed several classes of bent functions from quadratic permutations and permutations with Niho exponents. In this paper, we further investigate one of these classes of bent functions, establishing more general sufficient conditions and discussing their relationship with the class of Maiorana–McFarland bent functions.

In this paper, we investigate two-point Algebraic Geometry codes associated to the Skabelund maximal curve constructed as a cyclic cover of the Suzuki curve. In order to estimate the minimum distance of such codes, we make use of the generalized order bound introduced by P. Beelen and determine certain two-point Weierstrass semigroups of the curve.

Hermitian functional and differential codes are AG-codes defined on a Hermitian curve. To ensure good performance, the divisors defining such AG-codes have to be carefully chosen, exploiting the rich combinatorial and algebraic properties of the Hermitian curves. In this paper, the case of differential codes CΩ(D, mT) on the Hermitian curve ℋq3 defined over Fq6 is worked out where su.yppp(T) := ℋq3(Fq2), the set of all Fq2-rational points of ℋq3, while D is taken, as usual, to be the sum of the points in the complementary set D = ℋq3(Fq6) \ℋq3(Fq2). For certain values of m, such codes CΩ(D, mT) have better minimum distance compared with true values of 1-point Hermitian codes. The automorphism group of CL(D, mT), m ≤ q3- 2, is isomorphic to P GU(3, q).