You can find general information about Hamming Codes and how to use them here and in the lecture slides.
The given generator matrix here is used for Assignment 2 and further, not the first one!
For this course we have input words of length 6.
Since we want to have SEC-DED features the resulting notation for our Hamming Code is $(11, 6)$.
The non-systematic generator matrix $G'_{6,10}$ to start with is provided by us.
\[
G' = \left( \begin{matrix}
1 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\
0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\
1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 \\
1 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 1 & 0 \\
1 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 1 \\
\end{matrix} \right)
\]