In the even order case, every oval can be uniquely extended to a set of n+2 points, no three of which are collinear. These sets are called hyperovals. The additional point, which is the common intersection of all the tangent lines to the oval, is called the nucleus of the oval (this point has also been called the knot and the strange point of the oval). A conic together with its nucleus is a hyperoval called a hyperconic (also known as a regular hyperoval or complete conic).
We shall restrict ourselves to the Desarguesian planes defined over the Galois Field GF(2h), and coordinatized in the standard way. To avoid the trivial, and sometimes exceptional case of the Fano plane, we shall assume when necessary that h> 1. Any hyperoval in such a plane contains at least 4 points, no three of which are collinear, and we may assume (by the Fundamental Theorem of Projective Geometry) that a hyperoval passes through the four points, (1,0,0), (0,1,0), (0,0,1) and (1,1,1). If is a hyperoval, it is thus completely determined by its affine points and we define: