= \left(
\begin{array}{cccccc}
G_{1,1} & G_{1,2} & G_{1,3} & \ldots & G_{1, l-1} & G_{1,l} \\
0 & G_{2,2} & G_{2,3} & \ldots & G_{2, l-1} & G_{2,l} \\
0 & 0 & G_{3,3} & \ldots & G_{3, l-1} & G_{3,l} \\
\vdots & \vdots & \vdots & \ddots & \vdots & \vdots \\
0 & 0 & 0 & \ldots & G_{l-1,l-1} & G_{l-1,l} \\
0 & 0 & 0 & \ldots & 0 & G_{l,l} \\
\end{array} \right).$$

The length of the code $ C $ is $ n = n_1 + n_2 + \cdots + n_l $ and its dimension is $ k = k_1 + k_2 + \cdots + k_l $. $ C $ is the cartesian product of the codes $ C_1, C_2, \ldots, C_l $ if $ G_{i,j} = 0 $, for all $ j > i $.

For a given reduction $ \mathcal{R} $ as in the previous definition, we define its main components as the codes $ C_1, C_2, \ldots, C_l $, its row components as the $ \mathbb{F}_{q^m} $-linear codes $ C_i^\prime \subseteq \mathbb{F}_{q^m}^n $ with generator matrices $$\label{row components}
G_i^\prime = (0, \ldots, 0, G_{i,i}, G_{i,i+1}, \ldots, G_{i,l}),$$ for $ 