A $(6,3)$ linear block code is specified by the generator matrix G as shown below.

$5$

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

$($i$)$ What is the minimum distance of the code?

$($ii$)$ What is the maximum number of errors this code car detect? What is the

maximum number of errors this code can correct?

$($iii$)$ Write the parity check matrix $H$ in systematic form for this code?

$($b$)$

For what values of $k$ does an $(6,k)$ cyclic code exist? List all possible $k\text{'}$s with

corresponding generator polynomial$($s$).$