Roth-Lempel code[1] 

Member of a \(q\)-ary linear code family that includes many examples of MDS codes that are not GRS codes.

The generator matrix of a Roth-Lempel code is \begin{align} G=\left(\begin{array}{cccccc} \alpha_{1}^{k-1} & \alpha_{2}^{k-1} & \cdots & \alpha_{n}^{k-1} & 1 & 0\\ \alpha_{1}^{k-2} & \alpha_{2}^{k-2} & \cdots & \alpha_{n}^{k-2} & 0 & 1\\ \vdots & \vdots & \ddots & \vdots & \vdots & \vdots\\ \alpha_{1}^{2} & \alpha_{2}^{2} & \cdots & \alpha_{n}^{2} & 0 & 0\\ \alpha_{1} & \alpha_{2} & \cdots & \alpha_{n} & 0 & 0\\ 1 & 1 & \cdots & 1 & 0 & 0 \end{array}\right)~, \tag*{(1)}\end{align} where \(\{\alpha_j\}\) is a set of elements of \(GF(q)\). The code is MDS if no subset of \(k-1\) elements sums to zero.