geo909

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	98 reputation	bio	website		visits	member for	1 year, 1 month
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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 22	accepted	Are linear shift register sequences corresponding to reciprocal polynomials equivalent?
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	revised	Are linear shift register sequences corresponding to reciprocal polynomials equivalent? I think "sequences" is also a relevant tag..
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..
Feb 5	asked	Are linear shift register sequences corresponding to reciprocal polynomials equivalent?
Dec 12	awarded	Commentator
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 12	accepted	Can every periodic binary sequence be expressed as the output of a Linear or Non-Linear Feedback Shift Register?
Dec 12	revised	Can every periodic binary sequence be expressed as the output of a Linear or Non-Linear Feedback Shift Register? added 5 characters in body
Dec 11	revised	Can every periodic binary sequence be expressed as the output of a Linear or Non-Linear Feedback Shift Register? added 321 characters in body
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 $N$?
Dec 11	revised	Can every periodic binary sequence be expressed as the output of a Linear or Non-Linear Feedback Shift Register? Inserted partial answer that I found
Dec 11	revised	LFSR (Linear Feedback Shift Register) title: added space between "LFSR" and rest of sentence
Dec 11	suggested	suggested edit on LFSR (Linear Feedback Shift Register)
Dec 11	asked	Can every periodic binary sequence be expressed as the output of a Linear or Non-Linear Feedback Shift Register?
Dec 11	revised	LFSR (Linear Feedback Shift Register) In the title "LfSR" was used instead of "LFSR". No reason not to capitalize f.
Dec 11	suggested	suggested edit on LFSR (Linear Feedback Shift Register)
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..