On the size of arcs in projective spaces

Abstract

The known results on the maximum size of an arc in a projective space or equivalently the maximum length of a maximum distance separable linear code are surveyed. It is then shown that this maximum is q+1 for all dimensions up to q in the cases that q=11 and q=13; the result for q=11 was previously known. The strategy is to first show that a 11-arc in PG (3,11) and a 12-arc in PG (3,13) are subsets of a twisted cubic, that is, a normal rational curve.