Take for example, I have a generator set that is linear binary code...
$\langle0011101_2, 0101011_2, 1000111_2\rangle$
And I would transform this to a Generator Matrix... (No full row or column of '0's)
\begin{bmatrix}0&0&1&1&1&0&1\\0&1&0&1&0&1&1\\1&0&0&0&1&1&1\end{bmatrix}
How would I go about converting this to a Standard Partition Form Generator Matrix?
The only vague understanding I have so far, is to have the portion 'm x m', where 'm' = rows, arranged to a identity matrix such as...
\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}
So the questions on my mind really are... Do i need to work out all the possible codes given a generator set before I can create a generator matrix? And how do i go about converting the generator matrix to a standard partition form?
I have done a fair amount of lookup online, however I couldn't really grasp the understanding, any help here would be greatly appreciated, thanks!