Ovals in $${\mathbb {Z}}^2_{2p}$$

Ovals in Desarguesian planes

This paper surveys the known ovals in Desarguesian of even order, making use of the connection between ovals and hyperovals. First the known hyperovals are and the inequivalent m of small order arc found. The ovals contained in each of the known are determined and presented in a uniform way. Computer for new hyperovals reported. 1. OVALS AND HYPEROVALS Let PG(2, q) be the 'DC," "<"""'0" -:)"t, ...

Ovoids and Translation Ovals

An oŠoid in a 3-dimensional projective geometry PG(3, q) over the field GF(q), where q is a prime power, is a set of q#­1 points no three of which are collinear. Because of their connections with other combinatorial structures ovoids are of interest to mathematicians in a variety of fields ; for from an ovoid one can construct an inversive plane [3], a generalised quadrangle [11], and if q is e...

Baer Subplanes, Ovals and Unitals

Bent functions and line ovals

In this paper we study those bent functions which are linear on elements of spreads, their connections with ovals and line ovals, and we give descriptions of their dual bent functions. In particular, we give a geometric characterization of Niho bent functions and of their duals, we give explicit formula for the dual bent function and present direct connections with ovals and line ovals. We also...

$\mathbb{Z}_{q}(\mathbb{Z}_{q}+u\mathbb{Z}_{q})$-Linear Skew Constacyclic Codes

In this paper, we study skew constacyclic codes over the ring ZqR where R = Zq + uZq, q = p s for a prime p and u2 = 0. We give the definition of these codes as subsets of the ring ZqR . Some structural properties of the skew polynomial ring R[x, θ] are discussed, where θ is an automorphism of R. We describe the generator polynomials of skew constacyclic codes over R and ZqR. Using Gray images ...