A Geometric Construction of Complete (kr ,r)-arcs in PG(2,7) and the Related projective [n,3,d]7 Codes

Abstract

A (k ,r)-arc is a set of k points of a projective plane PG(2,q) such that some r, but no r + 1 of them, are collinear. The (k ,r)-arc is complete if it is not contained in a (k + 1,r)-arc. In this paper we give geometrical construction of complete (k r ,r)-arcs in PG(2,7), r = 2,3,…, 7, and the related projective [n,3,d]7 codes.