CRC can only detect bust error of length m if the generator polynomial is of degree m. If you can recall how we generate the CRC for a particular message.
1.Both sender and receiver agree on a generator polynomial of degree say m.
2. sender appends m zero bits to the message.
2. sender finds the reminder of the binary division of the message with the generator polynomial (Note: the reminder can be of the length at most m).
3. sender appends the remainder to the message and send it to the receiver.
4. receiver again divides the message with the generator polynomial and see if the reminder is zero.
5. since we need to change at least m+1 bits to make the message with CRC code have zero reminder when divided by the polynomial. I can detect all busrt errors of length m.
