Scattered subspaces and related codes

After a seminal paper by Shekeey (Adv Math Commun 10(3):475-488, 2016), connection between maximum h-scattered $${{\mathbb {F}}}_{q}$$ -subspaces of $$V(r,q^n)$$ and rank distance (MRD) codes has been established in the extremal cases $$h=1$$ $$h=r-1$$ . In this paper, we propose for any $$h\in \{1,\ldots ,r-1\}$$ , extending unifying all previously known ones. As consequence, obtain examples non-square MRD which are not equivalent to generalized Gabidulin or twisted codes. We show that, up equivalence, having same parameters as ones our come from an subspace. Also, determine weight distribution related geometric counterpart subspaces.