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About: Mathematics of cyclic redundancy checks     Goto   Sponge   NotDistinct   Permalink

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The cyclic redundancy check (CRC) is based on division in the ring of polynomials over the finite field GF(2) (the integers modulo 2), that is, the set of polynomials where each coefficient is either zero or one, and arithmetic operations wrap around. Any string of bits can be interpreted as the coefficients of a message polynomial of this sort, and to find the CRC, we multiply the message polynomial by and then find the remainder when dividing by the degree- generator polynomial. The coefficients of the remainder polynomial are the bits of the CRC.