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Pseudonoise LFSR sequences of length $N = 2^k-1$ have the nice property that their cyclical autocorrelation is $N$ when the sequence is lined up with itself, and $-1$ elsewhere.

Is there a way to construct sequences of other lengths, that their cyclical correlation is close to $0$ or $-1$ when not lined up? If not, why not?

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    hmm, looks like there's a lot of research on this: http://signalslab.marstu.net/?page_id=17692012-04-05
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    Look for _Legendre sequences_ among others.2012-04-05
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    You're referring to Maximum Length Sequence (MLS), right? Truly random white noise has similar properties, I think any spectrally-white signal does, so maybe multitone signals would be appropriate? https://gist.github.com/endolith/53227342014-04-18
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    "The most commonly used sequences in direct-sequence spread spectrum systems are maximal length sequences, Gold codes, Kasami codes, and Barker codes." https://en.wikipedia.org/wiki/Pseudorandom_noise2014-04-18
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    Now that I know a little more about this, Barker sequences are for non-periodic autocorrelation, while Legendre and MLS sequences are for periodic autocorrelation. Gold and Kasami codes are derived from MLS, so are presumably periodic. [What can be used instead of a Barker sequence?](http://people.math.sfu.ca/~jed/Papers/Jedwab.%20Barker%20Sequence%20Alternatives.%202008.pdf) explains alternatives.2014-04-29

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