galois.FLFSR.characteristic_poly

property galois.FLFSR.characteristic_poly : Poly

The characteristic polynomial \(c(x) = x^{n} - c_{n-1}x^{n-1} - c_{n-2}x^{n-2} - \dots - c_{1}x - c_{0}\) that defines the linear recurrent sequence.

Notes¶

The characteristic polynomial is the reciprocal of the feedback polynomial \(c(x) = x^n f(x^{-1})\).

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