galois.FLFSR.feedback_poly

property galois.FLFSR.feedback_poly : Poly

The feedback polynomial \(f(x) = 1 + a_1 x + a_2 x^2 + \dots + a_{n} x^{n}\).

Notes¶

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

Examples¶

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

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

In [3]: lfsr.feedback_poly
Out[3]: Poly(5x^4 + 3x^3 + x^2 + 1, GF(7))

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