finding primitive element of GF(2^m)

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xplore29
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.

回答(1 个)

xplore29
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

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