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It depends on what you are doing.

The cyclic redundancy check will only detect an error, while the hamming code can also correct many types of errors. However to perform this correction the extra error detection parity bits required in hamming code are many more than the bits needed for cyclic redundancy check, per data byte being checked.

Normally cyclic redundancy check is done on large block of data that can be resent or retried to get the correct block of data (e.g. telecommunication channels, disk sectors).

Normally hamming code is done on individual bytes or words of computer memory.

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Q: Is the cyclic redundancy check better than hamming code?
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