# How can we binarize Reed Solomon Codes?

I want to be able to take a $[n,k,d]$ Reed Solomon code over $GF(2^m)$ and convert it to a $[mn,mk,d]$ binary code. I was not exactly sure how to implement this. What I have tried so far is the following:

```
F.<t> = GF(8)
n = 8, k = 4
C = codes.GeneralizedReedSolomon(F.list(), k)
V = VectorSpace(F, 8)
D = V.subspace(C)
E = D.vector_space(GF(2),map = false)
```

and then I would let C_binarize = codes.LinearCode(E), but I get an error when I try to convert the vector space D from being over GF(8) to being over GF(2). I am not sure if this is the right method or if there is some simpler function to use? Any advice would be greatly appreciated!