Let V be an r-dimensional \({\mathbb{F}_{{q^n}}}\)-vector space. We call an \({\mathbb{F}_{q}}\)-subspace U of V h-scattered if U meets the h-dimensional \({\mathbb{F}_{{q^n}}}\)-subspaces of V in \({\mathbb{F}_{q}}\)-subspaces of dimension at most h. In 2000 Blokhuis and Lavrauw proved that \({\dim_{\mathbb{F}_{q}}}\) U ≤ rn/2 when U is 1-scattered. Sub-spaces attaining this bound have been investigated intensively because of their relations with projective two-weight codes and strongly regular graphs. MRD-codes with a maximum idealiser have also been linked to rn/2-dimensional 1-scattered subspaces and to n-dimensional (r − 1)-scattered subspaces.

In this paper we prove the upper bound rn/(h + 1) for the dimension of h-scattered subspaces, h > 1, and construct examples with this dimension. We study their intersection numbers with hyperplanes, introduce a duality relation among them, and study the equivalence problem of the corresponding linear sets.

令V为r维\（{\ mathbb {F} _ {{q ^ n}}} \）-向量空间。我们称之为\（{\ mathbb {F} _ {Q}} \） -subspace Ú的Vħ -分散如果ù满足ħ维\（{\ mathbb {F} _ {{Q ^ N}}} \）的-subspaces V在\（{\ mathbb {F} _ {q}} \）尺寸至多-subspaces ħ。在2000 Blokhuis和Lavrauw证明\（{\暗淡_ {\ mathbb {F} _ {Q}}} \） Ú ≤ RN / 2时ù是1个散点。由于与投影二权码和强正则图的关系，对达到此界限的子空间进行了深入研究。具有最大理想化器的MRD码也已链接到rn / 2维1个散布的子空间和n维（r -1）个散布的子空间。

在本文中，我们证明了h分散子空间的维度h > 1的上界rn /（h + 1），并构造了具有该维度的示例。我们研究它们与超平面的相交数，引入它们之间的对偶关系，并研究相应线性集的等价问题。