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Does a hamming code always corrects one error and detect 2 errors ?

  1. May 10, 2013 #1
    does a hamming code always corrects one error and detect 2 errors ? and is the distance always 3 ?
    I know that that is true for (7,4) hamming code but does that apply to a (11,7) or (15,11) ?
    if not please let me how to get the answers
     
  2. jcsd
  3. May 11, 2013 #2

    mfb

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    I think the Hamming distance of 3 is used for the definition of "Hamming code". You can use codes with more additional bits to get more error detection/correction, but (7,4), (15,11) and so on are always 2 bits detection / 1 bit correction.
     
  4. May 11, 2013 #3
    Hamming codes are class of codes that have [itex] (2^{m}-1, 2^{m}-m-1,3) [/itex] which means that they all correct one and only one error. I don't know about detection of those other two, I am not familiar with that. But the distance of 3 dictates that they can correct only one error.
     
  5. May 11, 2013 #4
    sorry I meant is the minimum distance always 3 ?
     
  6. May 11, 2013 #5
    For class of Hamming codes, yes.
     
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