Page "Cyclic redundancy check" Paragraph 73

The advantage of choosing a primitive polynomial as the generator for a CRC code is that the resulting code has maximal total block length.

If r is the degree of the primitive generator polynomial, then the maximal total block length is, and the associated code is able to detect any single-bit or double-bit errors.

We can improve this situation.

If we use the generator polynomial, where is a primitive polynomial of degree, then the maximal total block length is, and the code is able to detect single, double, and triple errors.