 Linear-feedback shift register

A binary linear-feedback shift register of degree $d$ updates a $d$-bit state by shifting and inserting a fixed linear combination over ${\mathbb{F}}_2$. With recurrenceits feedback polynomial is $x^d+a_{d-1}{x}^{d-1}+\cdots +a_0$.

A Linear Feedback Shift Register (LFSR) is a type of sequential circuit that consists of a shift register and a linear feedback mechanism. It is widely used in digital systems for a variety of applications, including pseudorandom number generation, cryptography, error detection and correction, and digital signal processing.