

Example:
Generator polynomial: 1001 has the factor 11
How to check if gen. polyn. contains the factor "x+1" (= 11):
Divide by 11:
111

11 / 1001
11

10
11

11
11

0 < That means: 1001 = 11 × 111
in other words: 1001 contains the factor "x+1"


10001 11001 11 11   10001 11001 10001 11001  XOR  XOR 110011 101011 ^^^^^^ ^^^^^^ 4 (even) 1's 4 (even) 1's 
Why this is so:


Because:
bitstring × P = bitstring × P' × 11 // P has the factor 11 ! = bitstring' × 11 ==> has an even # 1 bits !!! 



Error polynomial representing kconsecutive errors: 1111..1 <> k bits Generator polynomial = 1.........1 <> n+1 bits The division:  1.........1 / 1111..1 <> <> n+1 bits k bits will have a nonzero remainder if: k ≤ n 

Name  Generator polynomial 

CRCCCITT  10001000000100001 
CRC16  11000000000000101 
CRC32  100000100110000010001110110110111 