I'm trying to find the code words generated by this matrix and then decode some given words and find the bit with the error for this parity check matrix(H): $$ \begin{bmatrix} 1 & 0 & 1 & 1 & 0 & 0 \\ 1 & 1 & 0 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 1 \\ \end{bmatrix} $$
The encoded words are (011101), (110111), (111011), (111111).
The generator matrix (G) I got is:
$$ \begin{bmatrix} 1 & 0 & 0 & 1 & 0 & 1 \\ 0 & 1 & 0 & 1 & 1 & 0 \\ 0 & 0 & 1 & 1 & 1 & 1 \\ \end{bmatrix} $$
The encoded words I got (in order for 000, 001, 010,...,110, 111) are 000000, 001101, 010011, 011110, 100101, 101001, 110100, 111001. I'm unsure whether they're correct or not though as these are from a sample paper w/o solutions so any corrections would be appreciated.