property galois.FLFSR.characteristic_poly : Poly

The characteristic polynomial c(x)=xn−cn−1xn−1−cn−2xn−2−⋯−c1x−c0 that defines the linear recurrent sequence.

Notes

The characteristic polynomial is the reciprocal of the feedback polynomial c(x)=xnf(x−1).

Examples

In [1]: c = galois.primitive_poly(7, 4); c
Out[1]: Poly(x^4 + x^2 + 3x + 5, GF(7))

In [2]: lfsr = galois.FLFSR(c.reverse()); lfsr
Out[2]: <Fibonacci LFSR: f(x) = 5x^4 + 3x^3 + x^2 + 1 over GF(7)>

In [3]: lfsr.characteristic_poly
Out[3]: Poly(x^4 + x^2 + 3x + 5, GF(7))

In [4]: lfsr.characteristic_poly == lfsr.feedback_poly.reverse()
Out[4]: True