On Weighted Arcs of Type (n-q, n) in PG( 2, q )

Abstract

In this paper we proved that the existence of minimal ( 4q-2, q+4; f ) – arc of type ( 4, q+4 ), which having W is minimal and there is no point of weight greater than 2 in the projective plane of order q. Also we proved that the existence of (q+1+q(q+1)/2,2q+1;f) – arc of type (q+1,2q+1) in PG(2,q) where the points of weight 1 formed a conic, the points of weight 2 are the exterior points of the conic, the points of weight 0 are the interior points of the conic, W is minimal and Imf={0,1,2}.