Abstract: CRC (Cyclic Redundancy Check) codes are a widely used in digital data transmission and storage to ensure data integrity. The generic technique of these error-detecting codes consist of sending a block of data along with its checksum so that, the checksum of the received data can be calculated and compared to the original checksum. If they do not match then an error has occurred and steps are taken to recover the data.
We propose a recursive formula for computing the remainder of a Euclidean division of polynomials (with binary coefficients), which operates sequentially and in parallel. We use this formula in conjunction with a look-ahead scheme to design a fast CRC system.