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 spacePG(2n - 1,q),qodd, then there does not exist a spread ofPG(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 forqodd. It is also shown that the all one vector is not contained in the binary code spanned by the tangents to an elliptic quadric inPG(3,q),qodd. f1 E-mail: aart@win.tue.nl f2 The second author acknowledges the support of an Australian Postdoctoral Research Fellowship. E-mail: nick@maths.uq.edu.au f3 E-mail: wsdwhw@win.tue.n