Generator Polynomials
As can be seen the strength of any CRC code lies in it generator polynomial, G(x)
Three polynomials which are known for their low error rates are shown below along with the international standards which have adopted them:
CRC-12 = x12 + x11 + x3 + x2 + x1 + 1
CRC-16 = x16 + x15 + x2 + 1
CRC-CCITT = x16 + x12 + x5 + 1