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How do CRCs work?

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CRC (cyclic redundancy check) is one of the most common methods of error detection. It uses some interesting mathematical tricks to guarantee that it can catch certain kinds of errors. How does it work?

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00:00 - Detecting errors with modulo division
10:51 - Message data as a polynomial
16:41 - Finite fields
22:57 - Polynomial division
31:04 - Sending and verifying CRC
36:29 - Choosing a generator polynomial

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