Finite Fourier series and ovals in PG(2, 2^h)

Abstract

We propose the use of finite Fourier series as an alternative means of representing ovals in projective planes of even order. As an example to illustrate the method's potential, we show that the set [w 1

Vandermonde sets, hyperovals and Niho bent functions

“…where a 0 ∈ F , a i ∈ K and a q+1−i = a q i for 1 ≤ i ≤ q/2. In thesis [13], following ideas from [15], the ρ-polynomials were introduced. We note that the ρ-polynomials and g-functions are connected in the following way: g(u) = 1/ρ(u).…”

Polar coordinates view on KM-arcs

“…Following [9], consider an element i ∈ K with property T (i) = i + i q = 1. Then K = F (i) and i is a root of a quadratic equation…”

Equivalence classes of Niho bent functions

“…Remark 2.2. In thesis [26], following ideas from [30], the ρ-polynomials were introduced. We note that the ρ-polynomials and our g-functions are connected in the following way: g(u) = 1/ρ(u).…”

“…In order to use these theorems we need a presentation of the Payne hyperoval in the affine plane K = AG(2, q). The Payne hyperoval can be given [30] as…”