Constructs a Galois LFSR from its feedback polynomial \(f(x)\).

Parameters¶

feedback_poly: Poly¶

The feedback polynomial \(f(x) = -c_{0}x^{n} - c_{1}x^{n-1} - \dots - c_{n-2}x^{2} - c_{n-1}x + 1\).

state: ArrayLike | None = None¶

The initial state vector \(S = [S_0, S_1, \dots, S_{n-2}, S_{n-1}]\). The default is None which corresponds to all ones.

Notes¶

A Galois LFSR may be constructed from its characteristic polynomial \(c(x)\) by passing in its reciprocal as the feedback polynomial. This is because \(f(x) = x^n c(x^{-1})\).