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 Curious
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Mar
16
comment Finite field question involving the trace and a permutation.
Many thanks Jyrki, I'll need to study this a bit. I'll update later.
Mar
16
revised Finite field question involving the trace and a permutation.
added 364 characters in body
Mar
16
comment Finite field question involving the trace and a permutation.
I know a couple of people who were claiming that they could do math better after a couple of beers :) Anyway, I think I have an idea, but I have to double think before posting anything, I'm not sure yet.
Mar
10
revised Finite field question involving the trace and a permutation.
added 31 characters in body
Mar
10
comment Bijections of a finite field that preserve the kernel of the trace
I have realized what my $f(x)$ should be. Indeed, I was asking too much. If you want, check my updated question here: math.stackexchange.com/questions/1183155/…
Mar
10
asked Finite field question involving the trace and a permutation.
Feb
24
comment Bijections of a finite field that preserve the kernel of the trace
Thank you for your clear and thorough answer, I was quite off with my conjecture about these monomials. I will have to think how/if the question can be restated to suggest some other class of polynomials.
Feb
24
comment Bijections of a finite field that preserve the kernel of the trace
I think I was being quite careless when I wrote that title. It should be just bijections.
Feb
24
revised Bijections of a finite field that preserve the kernel of the trace
Changed the title as per my answer to a comment
Feb
24
accepted Bijections of a finite field that preserve the kernel of the trace
Feb
23
asked Bijections of a finite field that preserve the kernel of the trace
Jan
22
asked Is LU decomposition of matrices efficient for today's standards?
Jan
20
accepted Intersection of blocks of the symmetric BIBD $PG(d,q)$
Jul
9
accepted Which powers of a primitive element of a finite field yield a generator of a finite field extension?
Jul
7
comment Which powers of a primitive element of a finite field yield a generator of a finite field extension?
Thanks for your answer. Now, you say that WLOG, $i|(q^m-1)$, else $i$ is associate to a divisor's residue in $\Bbb{Z}_{q^m-1}$. Could you comment on that? I fail to understand it..
Jul
4
comment Which powers of a primitive element of a finite field yield a generator of a finite field extension?
Note that the last bullet is equivalent to "there is no $s$ such that $0<s<m$ and $\frac{q^m-1}{q-1}|i\frac{q^s-1}{q-1}$. So it follows that when $gcd(i,\frac{q^m-1}{q-1})=1$ this is true, but I couldn't prove that this is an if and only if condition
Jul
4
asked Which powers of a primitive element of a finite field yield a generator of a finite field extension?
Jul
2
awarded  Curious
Jun
28
awarded  Critic
Jun
27
accepted When is $c\alpha$ primitive, for nonzero $c\in GF(q)$ and $\alpha$ primitive in $GF(q^m)$?