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Apr
21
comment How can I construct the matrix representing a linear transformation of a 2x2 matrix to its transpose with respect to a given set of bases?
@ahorn That's a good point, Indeed my choice was arbitrary. I edited my answer to reflect this.
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
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
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/…
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.
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
Jun
27
comment Order of product of two elements in a group
$m,n$ should be $mn$ but edits have to have at least 6 characters changes, so I cannot edit
Apr
12
comment Linear independence of finite field elements and subfields
Thank you so much for the thorough answer, this is helpful.
Apr
12
comment Linear independence of finite field elements and subfields
Thanks Gerry, I should have been more careful. I updated the question.
Apr
9
comment Generalization of a projective plane?
Thanks, Quiaochu! I'll try to understand now how this generalizes the definition of a projective plane.
Apr
8
comment Generalization of a projective plane?
I can't create a tag, but I was wondering if it would make sense to have a "finite-geometry" tag.
Oct
26
comment Ordering compositions of integers, where cyclic shifts are not considered distinct
Please help me with the tags; I have < 300 reputation so I cannot create tags related to "integer compositions" "ordering", etc. Not sure what else to tag there.. Thank you.
Jul
8
comment References for this kind of combinatorial objects? (lists of integers with small number of distinct pairwise differences)
@AndréNicolas Didn't know about that problem.. That's very interesting.
Jul
8
comment References for this kind of combinatorial objects? (lists of integers with small number of distinct pairwise differences)
Thank you for the providing a on-the-spot theory, that helps a lot.
Feb
22
comment Are linear shift register sequences corresponding to reciprocal polynomials equivalent?
Thank you sir for helping me one more time with my understanding of LFSRs!
Feb
6
comment Are linear shift register sequences corresponding to reciprocal polynomials equivalent?
Thanks for the feedback! The definition according to the paper that I am reading ("Shift-Register Synthesis and BCH Decoding", by J.L. Masssey) is that the leading coefficient corresponds to the output bit. Now, regarding the reciprocal thing: Do you have any reference or hints about the proof? And furthermore, are you sure that this holds for non-maximal sequences (i.e. when the corresponding polynomial is non-primitive)?
Feb
5
comment Are linear shift register sequences corresponding to reciprocal polynomials equivalent?
Ah, no. I am studying LFSRs for their own sake, possibly later I'll see some applications in cryptography. In particular I was studying the Berlekamp-Massey algorithm which returns the connection polynomial of a given a sequence if enough elements of the sequence are given. The implementation in sage seems to return the reciprocal and I'm trying to figure out what gives.. That said, I find it kind of an interesting question on its own..
Dec
12
comment Can every periodic binary sequence be expressed as the output of a Linear or Non-Linear Feedback Shift Register?
Thanks, I have heard about those sequences but didn't know what they were.