This method applies to all generator polynomials used in CRC operations and BCH encoders. This transformation achieves a full speed-up compared to the serial architecture at the cost of an increase in hardware overhead.
First, this paper presents a mathematical proof of existence of a linear transformation to transform LFSR circuits into equivalent state space formulations. The contribution of this paper is two fold. Linear feedback shift register (LFSR) is an important component of the cyclic redundancy check (CRC) operations and BCH encoders.