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Organization: Alexa Crawls

Starting in 1996, Alexa Internet has been donating their crawl data to the Internet Archive. Flowing in every day, these data are added to the Wayback Machine after an embargo period.

Collection: Alexa Crawls

Starting in 1996, Alexa Internet has been donating their crawl data to the Internet Archive. Flowing in every day, these data are added to the Wayback Machine after an embargo period.

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Best CRC Polynomials

Philip Koopman, Carnegie Mellon University

Best CRCs | CRC Selection | CRC Zoo | Checksum and CRC Blog

These are the "Best" general-purpose CRC polynomials with specific Hamming Distance Properties. (See also: Notation and copyright statement). IMPORTANT NOTE: These are "BEST" polynomials under an assumption of a low, constant random independent BER such as you'd find in communication networks. If you have a BER that is higher than, say, 1 bit in 100,000, or is non-constant, or is non-random/non-independent, then you need to understand more before using these polynomials.

This data includes work-in-progress results.

CRC Summary Tables

Below is a table of CRC Polynomial performance by Hamming Distance. Click a CRC size for detailed information about CRC polynomials.

To use these tables: top number in each cell is maximum dataword length at that Hamming Distance. The bottom number in each cell is a "good" polynomial that gives at least that HD up to the indicated dataword length in implicit +1 notation. For example, the polynomial 0x247 is a 10-bit CRC that provides HD=4 (or better) up to 501 bit dataword length (501+10=511 bit codeword length). The corresponding polynomial is: 0x247=x^10 +x^7 +x^3 +x^2 +x +1, and is alternately known as 0x48f in explicit +1 notation. See the Polynomial Zoo for detailed information (or click the CRC size link at the top of each column). Additionally, see the tables below for more nuanced selection criteria.

Notes: minimum dataword length evaluated is 4 bits. Yellow highlighted cells indicated work in progress/missing data. Green indicates preliminary data subject to confirmation.

Notation:

• For details on interpreting the data rows and data file formats, see Hamming Weight Data notes section.
• *p - primitive polynomial. This has optimal length for HD=3, and good HD=2 performance above that length.
• *o - odd bit errors detected. This has a factor of (x+1) and detects all odd bit errors (implying that even number of bit errors have an elevated undetected error rate)
• *op - odd bit errors detected plus primitive. This is a primitive polynomial times (x+1). It has optimal length for HD=4, and detects all odd bit errors.

Additional note: the minimum length dataword considered is 4 bits due to the design of the search tool. (In other words, dataword lengths of 0, 1, 2, 3 bits are not analyzed. This does not affect results reported, but does mean there might, for example, be a 3-bit data word with higher HD than reported as the maximum HD possible for a particular polynomial.)

This web page and all data files are Copyrighted 2015 by Philip Koopman, Carnegie Mellon University.

This work is licensed under a Creative Commons Attribution 4.0 International License.

Please note that if any data errors or other issues are identified they will be updated at this page, but not necessarily anywhere that has copied these results. Therefore, you should always confirm at this URL: http://users.ece.cmu.edu/~koopman/crc/ that you have the most current version of data before using it.

Errata: (substantive changes that have been incorporated above):

• None to date