Abstract. By exploiting the connection between scattered [Formula: see text]-subspaces of [Formula: see text] and minimal nondegenerate 3-dimensional rank-metric codes of [Formula: see text], [Formula: see text], described in [ G. N. Alfarano et al., J. Combin. Theory Ser. A, 192 (2022), 105658 ], we will exhibit a new class of codes with parameters [Formula: see text] for infinite values of [Formula: see text] and [Formula: see text] odd. Moreover, by studying the geometric structures of these scattered subspaces, we determine the rank weight distribution of the associated codes.

A set $$T\subset {GF(q)}$$ , $$q=p^h$$ is a super-Vandermonde set if $$\sum _{y\in T} y^k=0$$ for $$0< k <|T|$$ . We determine the structure of super-Vandermonde sets of size $$p+1$$ (almost small) and size $$q/p-1$$ (almost large).