A generator matrix of (6,3) linear block code is given by

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

Determine

1. All the code vectors.
2. “d_min” for the above code.
3. Error detection and correction capability.
4. If the received sequence is 101101, determine the message bit sequence.