# Transform a list of coefficients to polynomial (in GF(2^8)) [closed]

Hi there,

Currently i'm trying to convert a list of coefficients automatically to a polynom. I got a list of zeros and ones and want to transform this list to a polynom in GF(2^8). First I set up the GF(2^8) with the reduction polynom

```
P2.<x> = GF(2)[];
p = x^8 + x^4 + x^3 + x + 1;
GF256 = GF(2^8, 'x', modulus=p)
```

Next I get a list of coefficients:

```
coeff = [0, 1, 0, 1, 1, 1, 0, 1]
```

which should be the polynom:

```
x^6 + x^4 + x^3 + x^2 + 1
```

How do I get this transformation from list to polynom automatically? The native thing I think about is I set up a string and fill in the coeff. like this:

```
polyString = str(coeff[7])+'*x^7 + '+str(coeff[6])...
```

And then cast it in GF256

```
poly = GF256(polyString)
```

But I think they are smarter ways out there.. Any ideas ? :)

Like that:

Hey. Thanks. I just need to reverse the list because the highest coefficient is the first item in my list. Thanks ;)