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The cyclic redundancy check is based on division in the ring of polynomials over the finite field GF , 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 x n {\displaystyle x^{n}} and then find the remainder when dividing by the degree- n {\displaystyle n} generator polynomial. The coefficients of the remainder polynomial are the bits of the CRC.
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