Editing Primitive polynomial (field theory) (section)

===CRC codes===
The [[cyclic redundancy check]] (CRC) is an error-detection code that operates by interpreting the message bitstring as the coefficients of a polynomial over GF(2) and dividing it by a fixed generator polynomial also over GF(2); see [[Mathematics of CRC]]. Primitive polynomials, or multiples of them, are sometimes a good choice for generator polynomials because they can reliably detect two bit errors that occur far apart in the message bitstring, up to a distance of {{nowrap|2<sup>''n''</sup> − 1}} for a degree ''n'' primitive polynomial.