150 reputation
9
bio website
location
age
visits member for 2 years, 9 months
seen yesterday

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.
Dec
12
comment Can every periodic binary sequence be expressed as the output of a Linear or Non-Linear Feedback Shift Register?
Indeed, my background was from the top of my head and wrong at times, I have corrected the parts of the question that were wrong, thanks. Indeed, I have been looking around and when it comes to the non-linear case things are messy. Finding NLFSR's with guaranteed long periods is apparently a notoriously hard problem and every now and then somebody may publish a paper examinning a specific family of such sequences, but this is definitely not a question that would get a straightforward answer. As you said, for the linear case, the minimal LFSR is given by the Berlekamp-Massey algorithm.
Dec
11
comment Can every periodic binary sequence be expressed as the output of a Linear or Non-Linear Feedback Shift Register?
You're right, that was trivial! Do you also know if we know anything about the minimal FSR which would output a given sequence? For instance, given a sequence with a (potentially huge) period 2^n-1 one can construct a LFSR with only $n$ stages that outputs this sequence.. Are there any similar in nature results for the general period $N$?
Nov
24
comment Subspaces, transformation matrices exercise
I think you will probably be downvoted soon unless you change some things: first, your question is not very well stated. "We define a matrix, where..". So, what is the matrix that we defined? Also you are using "n" as a vector of $\mathbb{R}^n$. It's better not to use the same letter for different things (although it's boldface). Another thing is that if you plan to continue using this site, invest a little bit of time learning the latex syntax. You may also want to use the "homework" tag here..
Nov
24
comment Is the QR algorithm for computing eigenvalues efficient for today's standards?
Thanks for the answer.. The additional information is very interesting too.
Nov
23
comment Is the QR algorithm for computing eigenvalues efficient for today's standards?
I'm sure it is implemented in matlab and other mathematical software if you call it explicitly but the point of my question wasn't exactly that.. Is it efficient for today's standards? Would it be used by software like matlab by default or is it considered kind of obsolete?
Oct
16
comment Using Lagrange's Interpolation Formula to show that boolean functions over finite fields are polynomials
Thanks. I guess they still have a typo for including 0 in their sum, though..