Linear Feedback Shift Register Taps

Question

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.

Answer 1

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.