$($i$)$ A repetition code of block length n is a simple code consisting of only two code words one $(0,0,...,0)$ and the other $(1,1,...,1),$ both n$-$bit. Find the parity check matrix and the generator matrix of this code in the systematic form.

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