to further confuse the matter, the paper by p. koopman and t. chakravarty converts crc generator polynomials to hexadecimal numbers in yet another way: msbit-first, but including the formula_1 coefficient and omitting the formula_28 coefficient. this "koopman" representation has the advantage that the degree can be determined from the hexadecimal form and the coefficients are easy to read off in left-to-right order. however, it is not used anywhere else and is not recommended due to the risk of confusion.