On the non-existence of Thas maximal arcs in odd order projective planes

In this paper it is shown that given a non-degenerate elliptic quadric in the projective space PG(2n - 1, q), q odd, then there does not exist a spread of PG(2n - 1, q) such that each element of the spread meets the quadric in a maximal totally singular subspace. An immediate consequence is that the construction of [9] does not give maximal arcs in projective planes for q odd. It is also shown that the all one vector is not contained in the binary code spanned by the tangents to an elliptic quadric in PG(3, q), q odd. (C) 1998 Academic Press.