Show that a code can correct d errors , only when it can detect 2d errors, d ∈N\in N.

I am taking a lecture in discrete mathematics and have the problem to show this statement. Has this anything to do with the Hamming distance? We just had one lesson and we did not even mention anything about the Hamming codes.

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Yes, it only requires the notion of “Hamming distance.” You want to look at the “radius” allowed when making errors. To detect errors, you just want to ensure the errors do not turn a codeword into another one. So, how many bits can you flip? To correct, you want the true codeword to be the unique closest one to the received bit string, so again how many bits can we flip?
– Michael
Oct 21 at 2:29

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