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Wikipedia's article Cyclic redundancy check states that for the same n (bits) there are multiple CRCs possible with different polynomial. Then it lists this Best CRC Polynomials article that gives some variations with different polynomials. I am looking to implement a simple CRC-8. What should be my criteria for picking one polynomial over another?

I assume that it boils down to selecting the Hamming distance, but how is that related to my problem at hand? How do I pick the correct/best Hamming distance for best detecting possible errors in my case (and in what terms should I describe my case)? For example, will the choice depend on the media for storing/transmitting data or other physical factors or something else?

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    $\begingroup$ Have you read this report, by the same author? tc.faa.gov/its/worldpac/techrpt/tc14-49.pdf $\endgroup$ – Yuval Filmus Mar 28 '16 at 7:52
  • $\begingroup$ No, thanks, that's what I was looking for (at the top of page C-19)! Please post it as an answer and I will be happy to accept it. I only wonder why the "best" polynomials listed at the bottom of page C-18 differ from those listed on users.ece.cmu.edu/~koopman/crc ? $\endgroup$ – Greg Mar 28 '16 at 13:10
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The author of the list that you mention has written a thorough report on the problem of selecting a CRC polynomial, which probably contains the answers to all your questions. See page C-19:

Important to select CRC polynomial based on:

  • Data Word length
  • Desired HD
  • Desired CRC size

Safety-critical applications commonly select HD=6 at max message length

For example, HD-6 detects between 1-6 error bits in the Data Word, so the bigger the HD the better (for the given Data Word length).

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