Existence and Non-existence ofm-systems of Polar Spaces

Abstract

In this paper, the m - systems of the finite polar spaces W2n+1(2), Q−(2n+ 1, 2), Q+(2 n+ 1, 2) and Q(2 n+ 2, 2) are classified for n= 1, 2, 3 and 4. As a consequence of this, symplectic translation planes of order 32 are classified, and some maximal arcs in these planes are constructed. Improvements of previous non-existence results on m -systems of W2n+1(q), Q−(2n+ 1, q) and H(2 n, q2) are also obtained.