the most interesting property of reciprocal polynomials, when used in crcs, is that they have exactly the same error-detecting strength as the polynomials they are reciprocals of. the reciprocal of a polynomial generates the same "codewords", only bit reversed — that is, if all but the first formula_2 bits of a codeword under the original polynomial are taken, reversed and used as a new message, the crc of that message under the reciprocal polynomial equals the reverse of the first formula_2 bits of the original codeword. but the reciprocal polynomial is not the same as the original polynomial, and the crcs generated using it are not the same (even modulo bit reversal) as those generated by the original polynomial.