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I'm trying to convert a generator matrix for a (10,4) code to standard form. (mod 2). I've looked for a while how to do this but I can't seem to find it.

Matrix is

$$ \begin{pmatrix} 1 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 1\\ 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1 & 0\\ 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1\\ 1 & 1 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 1\\ \end{pmatrix} $$

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    $\begingroup$ Gauss elimination will give a $4\times 10$ matrix of reduced echelon form $(I_4\mid A)$, where $I_4$ is the $4\times 4$ identity matrix. Note that if you need column permutations, then you will get a generator matrix for an equivalent linear code. $\endgroup$ – Wuestenfux Nov 1 '17 at 16:05
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I used Magma software to obtain the generator matrix in the standard form as follows.

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