Consider a (7,4) code whose generator matrix is

$G = b \begin{bmatrix} \ 1 & 1 & 1 & 1 & 0 & 0 & 0 \\ \ 1 & 0 & 1 & 0 & 1 & 0 & 0 \\ \ 0 & 1 & 1 & 0 & 0 & 1 & 0 \\ \ 1 & 1 & 0 & 0 & 0 & 0 & 1 \\ \end{bmatrix}$

i) Find H, the Parity- Check matrix of the code.

ii) Compute the syndrome for the received vector 1101101. Is this a valid code vector?