On cyclic k-arcs of Singer type in PG(2,q) Original Research Article

Let K be a k-arc in PG(2,q), q = pl, p prime, consisting of the points of a point orbit under a cyclic collineation group G. We show that if G is a subgroup of a Singer group of PG(2,q), if p is greater than 5, and if 2k is different from −2,1,2,4 (mod p), then k⩽(44/45)q+89.