property sdr.FLFSR.characteristic_poly : Poly

The characteristic polynomial \(c(x)\) that defines the linear recurrent sequence.

Notes

The characteristic polynomial \(c(x) = x^{n} - c_{n-1} \cdot x^{n-1} - c_{n-2} \cdot x^{n-2} - \dots - c_{1} \cdot x - c_{0}\) 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 = sdr.FLFSR(c); lfsr
Out[2]: <Fibonacci LFSR: c(x) = x^4 + x^2 + 3x + 5 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