Matrix Representation of Hamming Function

Matrix Representation of Hamming (7,4)

We have: $G(x_1,x_2,x_3,x_4)=(x_1,x_2,x_3,x_4,p_1,p_2,p_3)$

&\text{Identity matrix} \\ L_{1}^{T} & L_{2}^{T} & L_{3}^{T} & L_{4}^{T} \end{array}\right]$$ For our classic example, this was:

G = \left[\begin{array}{cc} 1 & 0 & 0 & 0\ 0 & 1 & 0 & 0\ 0 & 0 & 1 & 0\ 0 & 0 & 0 & 1\ 1 & 1 & 1 & 0\ 1 & 0 & 1 & 1\ 1 & 1 & 0 & 1\ \end{array}\right]