finding primitive element of GF(2^m)

Question

xplore29 2012-3-22

Hi

How can I find the primitive element (field generator) of a GF(2^m) where q=2^m.

The following code gives the roots of primitive polynomial for the specified GF(q)

n = q-1; a = gf(2,log2(n+1))

but i cannot figure out a way to confirm that the roots of primitive polynomial ARE the generators of the extension field.

I tried using a simple loop

for i=1:q-2

f(i)=mod(2^i,q-1);

end

sort(f)

hoping that this will show that the generator stepped through each element of the field but its not working......

Thanku.

Answer 1

xplore29 2012-3-22

correction:

b=a(1); %picking the first root of primitive polynomial for testing

for i=1:q-2

f(i)=mod(b^i,q-1);

end