equivalence. This connection is shown to extend and unify the previously known ones in Section \[sec:uni\]. Section \[sec:twocharact\] completes the connection between $h$-scattered subspaces of dimension $\frac{rn}{h+1}$ and MRD codes, by means of two characterizations which are proved through the ordinary and Delsarte dualities. Section \[sec:noGab\] provides families of MRD codes which are not equivalent to punctured generalized (twisted) Gabidulin codes. Section \[sec:h+1weights\] computes the weight distribution of the linear codes arising from $h$-scattered linear sets of rank $\frac{rn}{h+1}$, seen as projective systems. Finally, in Section \[sec:open\], we resume our results and state some open questions.

Preliminaries {#sec:pre}
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Scattered $\mathbb{F}_q$-subspaces with respect to $\mathbb{F}_{q^n}$-subspaces {#sec:h-scatt}
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Let $V=V(m,q)$ denote an $m$-dimensional ${{\mathbb F}}_q$-vector space. A $t$-spread of $V$ is a set ${{\mathcal S}}$ of $t$-dimensional ${{\mathbb F}}_q$-subspaces such that each vector of $V^*=V\setminus \{{\bf 0}\}$ is contained in exactly one element of ${{\mathcal S}}$. As shown by Segre in [@Segre], a $t$-spread of $V$ exists if and only if $t$ divides $m$.

Let $V$ be an $r$-dimensional ${{\mathbb F}}_{q^n}$-vector space and let ${{\mathcal S}}$ be an $n$-spread of $V$. An ${{\mathbb F}}_q$-subspace $U$ of $V$ is called *scattered* w.r.t. ${{\mathcal S}}$ if $U$ meets every element of ${{\mathcal S}}$ 