<algorithm> (CRC or "cyclic redundancy code") A number derived from, and stored or transmitted with, a block of data in order to detect corruption. By recalculating the CRC and comparing it to the value originally transmitted, the receiver can detect some types of transmission errors.
The CRC is "redundant" in that it adds no information. A single corrupted bit in the data will result in a one bit change in the calculated CRC but multiple corrupted bits may cancel each other out.
CRCs treat blocks of input bits as coefficient-sets for polynomials. E.g., binary 10100000 implies the polynomial: 1*x^7 + 0*x^6 + 1*x^5 + 0*x^4 + 0*x^3 + 0*x^2 + 0*x^1 + 0*x^0. This is the "message polynomial". A second polynomial, with constant coefficients, is called the "generator polynomial". This is divided into the message polynomial, giving a quotient and remainder. The coefficients of the remainder form the bits of the final CRC. So, an order-33 generator polynomial is necessary to generate a 32-bit CRC. The exact bit-set used for the generator polynomial will naturally affect the CRC that is computed.
Most CRC implementations seem to operate 8 bits at a time by building a table of 256 entries, representing all 256 possible 8-bit byte combinations, and determining the effect that each byte will have. CRCs are then computed using an input byte to select a 16- or 32-bit value from the table. This value is then used to update the CRC.