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| visits | member for | 1 year, 1 month |
| seen | May 19 at 19:35 | |
| stats | profile views | 9 |
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Feb 22 |
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Are linear shift register sequences corresponding to reciprocal polynomials equivalent? Thank you sir for helping me one more time with my understanding of LFSRs! |
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Feb 6 |
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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)? |
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Feb 5 |
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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.. |
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Dec 12 |
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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. |
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Dec 12 |
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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. |
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Dec 11 |
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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 $N$? |
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Nov 24 |
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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.. |
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Nov 24 |
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Is the QR algorithm for computing eigenvalues efficient for today's standards? Thanks for the answer.. The additional information is very interesting too. |
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Nov 23 |
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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? |
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Oct 16 |
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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.. |
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Oct 12 |
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Using Lagrange's Interpolation Formula to show that boolean functions over finite fields are polynomials Thanks you. What you say makes sense.. In fact, in a different part of this book they justify something very similar to the equation that you mentioned. There is one issue that still worries me. It seems to me that the text has a typo: $k$ should start from $1$ instead of $0$ as you stated (or end in $2^n-2$ instead of $2^n-1$). The problem is that they use the formula with $k$ starting from $0$ in order to do other things.. Can you confirm that it is a typo and your version ($k$ starts from $1$) is correct? So far I have been confirming that but maybe I'm wrong.. |
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Sep 18 |
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Row reduction over any field? You're right, I now realize that the question was confused on the first place! Apparently I'm quite confused myself! I will look into it and I'll correct the question soon. Thanks |
