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I am trying to put things in places on the use of Hamming Distance (HD) in error detection and correction in Computer Networks. I'm looking for correction/verification on the following:

HD is a measure of how well the error-detection/correction can/did perform. It is not an error detection or correction method by itself.

Part of the input to HD is the code-words-- the set of valid codes, say set $C$ that are to be transmitted. With this code-set at hand, $d_{min}$, is the minimum of HDs between any two word pairs in $C$.

What HD tells is,

In this code set $C$, the best that an error detection algorithm can do is

  • to detect ($d_{min}-1$)-bit errors, i.e., errors in which $d_{min}-1$ of the bits are flipped,

and

  • to correct ($(d_{min}-1)/2$)-bit errors.

Hamming Distance is a method to set the boundaries how well an error-detection/correction scheme can do on a specific case (specific set of messages transmitted). HD itself isn't an error-detection/correction scheme by itself.

Am I missing anything here?

TIA.

Please note: I've seen some useful discussions including Hamming distance required for error detection and correction and Hamming distance necessary for detecting d-bit error and for correcting a d-bit error.

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EDIT:

HD is a scheme that has use in many contexts that the coding theory applies.

This Q is about the use of Hamming Distance in error detection/correction in Communication Networks.

More specifically-- consider a stream of bits transmitted by a node on one end of a link to the node on the other end of that link.

What use is it here? Other than telling how well a particular detection/correction method can do on an assumed set of messages transmitted in that stream.

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EDIT 2:

Figured this -- this was an early Q in not-enough-time.

Not letting me to delete the Q.

Thanks all.

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Your terminology is a bit off. Hamming distance is a metric on words given by the number of different symbols. The minimal distance of a code is the minimal (Hamming) distance between two different codewords, and enjoys the properties you listed.

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