Given is the following generator matrix which represents a linear code $C \subseteq \mathbb F_2^8$:
$$G=\left( \begin{array}{rrr} 1 & 0 & 0 & 1 & 1 \\ 0 & 1 & 0 & 0 & 1\\ 1 & 1 & 1 & 1 & 0\\ \end{array}\right)$$
I have to compute the check matrix $H$ which is defined as $H=[-P^T | I_{n-k}]$, this should be no problem, but since $G$ is not in the form $G=[I_k | P]$ which is required for $H$ i do not know how to do that.
Is it possible to somewhat rewrite $G$ such that $G$ contains $I_3$ without losing any information?
Thank you very much!