be a finite projective plane of order q (not necessarily desarguesian).
Some authors permit the degree of a maximal arc to be 1, q or even q+ 1.
[1] Letting K be a maximal (k, d)-arc in a projective plane of order q, if All of these cases are considered to be trivial examples of maximal arcs, existing in any type of projective plane for any value of q.
When 2 ≤ d ≤ q- 1, the maximal arc is called non-trivial, and the definition given above and the properties listed below all refer to non-trivial maximal arcs.
One can construct partial geometries, derived from maximal arcs:[5]