The Construction of Complete (k,4)-Arcs in PG(2,8) on projective plane over Galois Field GF (8)

Abstract

In this work, we construct by an algebraic method the projectively distinct (k,4)-arcs in PG(2,8),where k 5 and we prove that the complete (k,4)-arcs do not exist , when 5 k 18 . Also we find that complete (k,4)-arc in PG(2,8) is the (20,4)-arc an complete (k,3)-arc and PG(2,8)is the (19,4)-arc .