Maximal Arcs

Some articles on maximal arcs, arcs, maximal, maximal arc, arc:

Maximal Arc - Definition
... Maximal arcs of degree d ( 2 ≤ d ≤ q- 1) are (k,d)-arcs in, where k is maximal with respect to the parameter d, in other words, k = qd + d - q ... Equivalently, one can define maximal arcs of degree d in as non-empty sets of points K such that every line intersects the set either in 0 or d points ... Some authors permit the degree of a maximal arc to be 1, q or even q+ 1 ...
Maximal Arc - Properties
... The number of lines through a fixed point p, not on a maximal arc K, intersecting K in d points, equals ... In the special case of d = 2, maximal arcs are known as hyperovals which can only exist if q is even ... An arc K having one fewer point than a maximal arc can always be uniquely extended to a maximal arc by adding to K the point at which all the lines meeting K in d - 1 points meet ...