32-bit cyclic redundancy codes for Internet applications

Standardized 32-bit Cyclic Redundancy Codes provide fewer bits of guaranteed error detection than they could, achieving a Hamming Distance (HD) of only 4 for maximum-length Ethernet messages, whereas HD=6 is possible. Although research has revealed improved codes, exploring the entire design space has previously, been computationally intractable, even for special-purpose hardware, Moreover, no CRC polynomial has yet been found that satisfies an emerging need to attain both HD=6 for 12K bit messages and HD=4 for message lengths beyond 64K bits. This paper presents results from the first exhaustive search of the 32-bit CRC design space. Results from previous research are validated and extended to include identifying all polynomials achieving a better HD than the IEEE 802.3 CRC-32 polynomial. A new class of polynomials is identified that provides HD=6 up to nearly, 16K hit and HD=4 up to 114K bit message lengths, providing the best achievable design point that maximizes error detection for both legacy, and new applications, including potentially iSCSI and application-implemented error checks.