Some Standard Polynomial Codes

16 bit checksums catch -

• all single and double bit errors
• all errors with an odd number of bits
• all burst errors ≤ 16 bits long
• 99.997% of burst errors = 17 bits
• 99.998% of burst errors ≥ 18 bits

   CRC-12 = x 12 + x 11 + x 3 + x 2 + x + 1

   CRC-16 = x 16 + x 15 + x 2 + 1

CRC-CCITT = x 16 + x 12 + x 5 + 1

   CRC-32 = x 32 + x 26 + x 23 + x 22 + x 16 + x 12 + x 11 + x 10 +
            x 8 + x 7 + x 5 + x 4 + x 2 + x + 1

CRCs are often performed in hardware, for example the DEC-VAX architecture (mid-1980s) had an assembly language instruction to perform CRC-16 (!).

Today, all network interface cards (such as wired and wireless Ethernet) perform checksumming "on-board".