Consider the following matrix $$ G:=\left[ \begin {array}{cccccccc} 1&0&0&0&\alpha&\alpha+1&1&1\\ 0&1&0&0&1&\alpha&\alpha+1&1\\ 0&0&1&0&1&1&\alpha&\alpha+1\\ 0&0&0&1&\alpha+1&1&1& \alpha\end {array} \right] $$
where entries of matrix $G$ come from finite field $GF(2^8)$ such that this finite field is constructed by the polynomial ${\alpha}^{8}+{\alpha}^{4}+{\alpha}^{3}+\alpha+1$.
My question: How to define matrix $G$ in the MAGMA software such that we can see the coding parameters that are generated with the matrix $G$?
At First, we should define the finite field $GF(2^8)$ by our polynomial as follows
$$ K<x>:=ExtensionField< GF(2), z | z^8+z^4+z^3+z+1 >; $$
After that we have to define matrix space over the finite field $K$, in the following form
$$ M := KMatrixSpace(K, 4, 8); $$ Now, we define our matrix as shown
$$ G := M ! [1,0,0,0,x,x+1,1,1,0,1,0,0,1,x,x+1,1,0,0,1,0,1,1,x,x+1,0,0,0,1,x+1,1,1,x]; $$
In continue, we find coding parametr of $G$, by this command
$$ C := LinearCode(G); $$
I asked two questions about math software in the Math stack. The first question was about Maple that no one answer and because of this I asked from support team of Maple. The next question that you can see was about Magma that again no one answer and I read two chapters of Magma guide to find it's method.
I strongly believed that Math software tags of math stack should be independent of math stack and it's better that defined a separate forum for this special tags.