${?}^T$ The parity generator matrix for a Hamming $(8,4)$ code is given by

$G_{{?}_{?}}=\left[\begin{array}{cccc}0& 1& 1& 1\\ 1& 0& 1& 1\\ 1& 1& 0& 1\\ 1& 1& 1& 0\end{array}\right]$

$($a$)$ Compute the distance between all pairs of code words and show the

distance of the code is $4.$ You may use MATLAB to do this.

$($b$)$ Show that the difference between any pair of code words is a code

word.