Classification of K-ARCS in projective plane over galois field.

The purpose of this thesis is to study the classification of k-arcs in the projective plane PG(2,11). A k-arc K in a finite projective plane is a set of k points, no three of which are collinear. A k-arc is complete if it is not contained in a (k+l)-arc. The maximum number of points that a k-arc can have is (p + 1) for p odd, a k-arc with this number of points is an oval. In this thesis we found the value of m(2,11) and construction of k-arcs in PG(2.11), where m(2.11) is the maximum value of k for which a k-arc exists in PG(2,11). Complete k-arcs in PG(2,11) for 4 < k < 7 do not exist, also complete k-arcs for k -11 do not exist. Moreover, we found that 12-arc is an oval that represents a conic in the plane. Finally, we classified the groups of the construction k-arcs for 4