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

Parameters:¶

feedback_poly: Poly¶

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

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 \(f(x) = x^n c(x^{-1})\).