Weighted (k,n)-arcs in the projective plane of order nine

Abstract

In this study the presence of (k,n;f)-arcs of two characters (m,n) in the Projective Plane of order 9 was investigated.The example of (85,13;f)-arcs of type (10,13) with the number of points of weight 0 is 6 was discussed. It was proved that there is no (85,13;f)-arc when the points of weight 0 form a (6,3)-arcs in PG(2,9). It was proved that there are two examples of (85,13;f)-arcs of type (10,13) when the points of weight 0 form a 6-arc which lies on a conic.The example of (81,12;f)-arcs of type (9,12) with the number of points of weight 0 is 10 was discussed. It was proved that there is no (81,12;f)-arc when the points of weight 0 form a a conic or a (10,3)-arc in PG(2,9).