Re: ffgen

["Eric J. Van der Velden" <ericjvandervelden@gmail.com>]

Hi Bill,

Thanks! I will try ffprimroot.

I am sorry, I do not know the term "field generator". Do you mean like i in F₉, which is of order 4, but 1 and i are a vectorspace basis over F₃ of F₉? 

Thanks.

On Wed, Jul 12, 2017 at 11:17 PM, Bill Allombert <Bill.Allombert@math.u-bordeaux.fr> wrote:

On Wed, Jul 12, 2017 at 09:37:10PM +0200, Eric J. Van der Velden wrote:
> I wanted to create a generator for F16. But ffinit gives a polynomial of
> order 5. So g is not a generator of F16*.
>
> ? g=ffgen([2,4],t)
> %161 = t
> ? g.mod
> %163 = t^4 + t^3 + t^2 + t + 1
> ? g^5
> %167 = 1
>
> So my first question is why ffinit comes up with a order 5 polynomial.

g is a field generator. If you want a group generator use

h=ffprimroot(g)

? g=ffgen([2,4],t)
%1 = t
? fforder(g)
%2 = 5
? h=ffprimroot(g)
%3 = t^3+t^2+t
? fforder(h)
%4 = 15

Cheers,
Bill.