الملخص

ABSTRACT In this paper we finding the maximum(k,r)-arcs and minimum values for a complete(k,r)-arcs which are unknown at yet in projective plane PG(2,31), improvement some of the maximum value mr(2,q) for 3≤r≤10 by using conic equation, and for value 4≤r≤6 by using incidence matrix and we get new examples (68,4), (96,5), (128,6)-arcs that have not been obtained previously. Also we prove that nonexists (k,3)-arcs when in PG(2,31) theorm (1.9.1).