On 2012-03-21, clinton bowen <clinton.bo...@gmail.com> wrote:
> Is there a way to derive irreducible polynomials of degree n for the field F
> 2? I am looking for the set of all irreducible polynomials of degree n=31. 
This is a huge set... IMHO blindly generating it in reasonable time is out of
the question. What kind of task do you want to do with them?

>  If so, how is it done in sage?

surely you can get one such polynomial, e.g.:

sage: f=GF(2^31,'a')
sage: f.polynomial()
a^31 + a^3 + 1

This one is used to define f as F_2[a]/(a^31 + a^3 + 1)

Best,
Dmitrii

>
> Thanks,
>
> clinton 
>

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