Consider a generator matrix $G$ for a nonsystematic $(6,3)$ code:

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

a$-$ Convert $G$ to systematic form, then find $H.$

b$-$ Construct the code for this $G,$ and show that $d$ min, the minimum distance between

codewords, is $3.$ Consequently, this code can correct at least one error.