Evasive subspaces

Let V denote an r-dimensional vector space over F q n , the finite field of elements. Then is also r n-dimension . An -subspace U ( h k ) -evasive if it meets h-dimensional -subspaces in dimension at most k. The 1 subspaces are known as scattered and they have been intensively studied geometry, their maximum size has proved to be ? ? 2 ? when even or = 3. We investigate subspaces, study two duality relations among them provide various constructions. In particular, we present first examples, for infinitely many values q, 3 5. obtain these examples characteristics 2,