The Generator matrix of (6,3) systematic block code is given below:

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

Find the code vectors, parity check matrix, and the error syndrome