\ldots & \beta_n^{[1]} \\
    \vdots & \vdots & \ddots & \vdots \\
    \beta_1^{[k-1]} & \beta_2^{[k-1]} & \ldots & \beta_n^{[k-1]} \\
    \end{array} \right)$$ has dimension $ k $ and minimum rank distance $ d_{R}(C_{Gab}) = n - k + 1 $, and hence is MRD. These codes are known as Gabidulin codes and were introduced in [@gabidulin]. Their GRWs were given in [@rgrw Cor. 2]: $$d_{R,r}(C_{Gab}) = n - k + r.$$

2.  Assume $ n = lm $ and $ k = lk^\prime $, for some positive integers $ l $ and $ k^\prime \leq m $: The $ \mathbb{F}_{q^m} $-linear code $ C \subseteq \mathbb{F}_{q^m}^n $ defined as $ C = C_1 \times C_2 \times \cdots \times C_l $, where each $ C_i \subseteq \mathbb{F}_{q^m}^m $ is a $ k^\prime $-dimensional Gabidulin code, has dimension $ k $ and minimum rank distance $ d_{R}(C) = m - k^\prime + 1 $, and hence is also MRD. These codes were introduced in [@reducible Cor. 1] and considered in [@silva-universal Sec. VII-C] for secure network coding. In contrast with Gabidulin codes, although a first analysis of these codes is given in [@silva-universal], their GRWs are still not known. We will find 