$(10$ points$)$ Assign messages to the words in $F_2^3$ as follows:

$000,100,010,001,110,101,011,111$

$ACDEGiN,0$

Let $C$ be the binary linear code with generator matrix

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

Use $G$ to encode the message "ENCODING".