# Linear Feedback Shift Register Taps

Linear feedback shift register tap charts are availale for registers of length 3 to 168. Does anyone have a chart for register lengths from 168 to 256 or beyond? Thank you.

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When I need something on that tune I might use Jörg's useful and ugly page of mathematical data.

In particular, all-trinomial-primpoly gives primitive GF(2) trinomials (LFSR with 2 taps, the minimum number) to degree 400. 100,63,0 tells you that $x^{100}+x^{63}+1$ is primitive, meaning the same as 100|100,63 at LFSR Feedback Taps to 168 bits.

Also of interest is eq-primpoly-w5, giving one primitive pentanomial (LFSR with 4 taps) per degree up to 660. The entry 660 498 329 164 0 tells that $x^{660}+x^{498}+x^{329}+x^{164}+1$ is primitive (equivalent to 660|660,498,329,164 in a Feedback Taps table). Reference is given to: Janusz Rajski et Jerzy Tyszer, Primitive Polynomials Over GF(2) of Degree up to 660 with Uniformly Distributed Coefficients.

Further, highbit-normalprimpoly gives one primitive polynomial per degree up to 400, selected has having the lowest non-constant term as high as possible. That one is handy for software implementations, for the representation of the polynomials can be compressed into a small bitmask.

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Not the easy look-up chart I was looking for but interesting none-the-less. Thank you. – William Hird May 25 '12 at 7:41
Any pointer to some "easy look-up chart", even to low order, just to have a feeling of what you find easy? – fgrieu 1 hour ago – fgrieu May 25 '12 at 11:18
Google LFSR Taps to 168 bits. You will see the chart. Sorry I don't know how to hyperlink :-( – William Hird May 25 '12 at 16:56
That looks good, thanks again! – William Hird May 25 '12 at 23:15
@WilliamHird: I have integrated more material in the answer. You have the option to assert that it is useful, or even that it answers the question, using buttons on the left of the answer's text. – fgrieu May 26 '12 at 10:36