CRC Hamming Weight Data

Philip Koopman, Carnegie Mellon University

Below is available data for CRC polynomial error detection effectiveness for a "zoo" of CRC polynomials. For relevant papers describing the research that producfed this data and how to use the data, please see this list of publications (link). Also, you can find additional information and pointers to specific CRC uses and citations for sources of CRC polynomials over at wikipedia, which at last look had a high quality page on this topic.

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# Bits in CRC={3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, others, 64}

There are two versions of each file. The basic version has up to 1024 bit data word length. The txt.gz file has longer data words, with length depending on the CRC size, and is in gzip file format to reduce file size. The longer files cover at least 64K bit data word length. See the NOTES SECTION for how to interpret the data files and other info. All lengths are in terms of # of bits in the dataword (not bytes; not codeword length). So a length of "56" with an 8-bit CRC corresponds to 7 bytes of payload + 1 byte of CRC value=> 8 total bytes of codeword (56+8=> 64 bits).

Related web pages:

3 Bit CRCs:

4 Bit CRCs:

5 Bit CRCs:

6 Bit CRCs:

7 Bit CRCs:

8 Bit CRCs:

9 Bit CRCs:

10 Bit CRCs:

11 Bit CRCs:

12 Bit CRCs:

13 Bit CRCs:

14 Bit CRCs:

15 Bit CRCs:

16 Bit CRCs:

17 Bit CRCs:

18 Bit CRCs:

19 Bit CRCs:

20 Bit CRCs:

21 Bit CRCs:

22 Bit CRCs:

23 Bit CRCs:

24 Bit CRCs:

25 Bit CRCs:


26 Bit CRCs:


27 Bit CRCs:


28 Bit CRCs:


29 Bit CRCs:


30 Bit CRCs:


31 Bit CRCs:


32 Bit CRCs:


(NOTE: lengths above 32 bits use an experimental 64-bit version of the analysis program that has not been validated against external sources for >32 polynomials due to a general lack of available data. Factorization information has not been computed for these polynomials. So please use these results with caution. If you know of independent 64-bit CRC HW/HD calculation results please contact me so I can build confidence in these results. Thanks!)

33-63 Bit CRCs

64-Bit CRCs


Interpret the table entries as follows:

Interpret the data files as follows:


See Wikipedia for citations and sources of most names.

I'll try to update Wikipedia with citations as they become formalized if nobody beats me to it. I have checked pretty thoroughly, but a lot of work in this area is pretty obscure. If I find out one of them was published before me I will of course be happy to update the attribution.

I welcome correspondence and especially notification of any errors that might have crept into the work. However, I cannot provide free individual advice on CRCs via e-mail. From time to time I'll augment the data, but research funding for this topic is scarce, so it mostly gets done more or less as a hobby.

If you know of a standard polynomial (e.g., one in an ISO, IEC, or IEEE standard) not in the "zoo" above, please let me know and I'll add it as I have time. (Ideally, you should add it to Wikipedia and then let me know it is there so I can do a data run for it.) While I have spent significant effort on getting things right, this data is provided as-is and provide with out any warranty -- use at your own risk.

Optimal performance bounds for dataword lengths up to 2048 bits:

Note: this data is subject to revision based on some e-mail comments, so consider this draft material. The given data is OK, but might be missing some even better values in some cases.


I currently have a backlog of changes, updates, and so on stemming from e-mail correspondence. I'll publish attributions for those as I am able to process them. I sincerely appreciate the efforts of everyone who has double-checked and commented upon my work.

While the work on this web page is unfunded, I have been fortunate enough in the past to have funding on related research topics from FAA, General Motors, Honeywell, Bosch, Bombardier, the Pennsylvania Infrastructure Technology Alliance (PITA), and an NSF student fellowship. I appreciate their support. Nothing on this web page should be considered their opinion or recommendation.

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

Creative Commons License
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: that you have the most current version of data before using it.

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