### Binary fields

Hello, I would like to perform the following on a binary field, i.e. `GF(2^m)`

.

- Define a polynomial and solve the polynomial over a binary field.
- Convert an element of the binary field into a bit string.

For the first, I've tried the following:

```
K = GF(2^7,'a');
PK.<x>=K[]; #I've also tried "x = PolynomialRing(GF(2^7,'a'),'x').gen"
f = (a^6 + a^3 + a)*x^2 + (a^6 + a^4 + a^3)*x + (a^5 + a^4 + a^3 + a^2 + 1);
print f.roots();
```

But the error is `TypeError: unable to coerce from a finite field other than the prime subfield`

.

For the second, I ~~have no clue ~~would like to ~~the second. I have tried ~~know how finite field elements are stored in ~~vain to find some help online but was unable to, so if ~~SAGE, are they stored as vectors?

If you have any resources that could point me in the right direction, I'll be very thankful for your help!