On Plane Arcs Contained in Cubic Curves

AbstractIf the group H of the Fq-rational points of a non-singular cubic curve has even order, then the coset of a subgroup of H of index two is an arc in the Galois plane of order q. The completeness of such an arc has been proved, except for the case j=0, where j is the j-invariant of the underlying cubic curve. The aim of this paper is to settle the completeness problem for the exceptional case and to provide an alternative proof of the known results