Generalising the Scattered Property of Subspaces

Let V be an r-dimensional $${\mathbb{F}_{{q^n}}}$$ -vector space. We call $${\mathbb{F}_{q}}$$ -subspace U of h-scattered if meets the h-dimensional -subspaces in dimension at most h. In 2000 Blokhuis and Lavrauw proved that $${\dim_{\mathbb{F}_{q}}}$$ ? rn/2 when is 1-scattered. Sub-spaces attaining this bound have been investigated intensively because their relations with projective two-weight codes strongly regular graphs. MRD-codes a maximum idealiser also linked to rn/2-dimensional 1-scattered subspaces n-dimensional (r ? 1)-scattered subspaces. paper we prove upper rn/(h + 1) for subspaces, h > 1, construct examples dimension. study intersection numbers hyperplanes, introduce duality relation among them, equivalence problem corresponding linear sets.