How to find Generator Matrix from a given Parity Check Matrix? I'm given a Parity Check Matrix
\begin{bmatrix}0&1&1&1&1&0&0\\1&0&1&1&0&1&0\\ 1&1&0&1&0&0&1\end{bmatrix}
and I have to find the Generator Matrix of it.I spent many days try to solve it but I can't

This parity-check matrix is in the standard form $$[P^T|I_{n-k}]$$
The generator matrix is hence given by
$$G=[I_k|P]=\begin{bmatrix}
1 &0& 0& 0& 0& 1& 1\\ 0& 1& 0& 0& 1& 0& 1\\0& 0& 1& 0& 1& 1& 0\\ 0& 0& 0& 1& 1& 1& 1
\end{bmatrix}$$
You can verify that $GH^T=0$
