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If you REALLY want to know why CRC is the way it is from a mathematical point of view:

"The iSCSI CRC32C Digest and the Simultaneous Multiply and Divide Algorithm"
https://pdfs.semanticscholar.org/21b8/c594566f8ad0dba7b8e071705b8f865d5fff.pdf

To find the best CRC polynomial for your specific range of message lengths:
https://users.ece.cmu.edu/~koopman/crc/



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