Hamming Distance

A Geometric Interpretation of Error correcting Codes
  • Hamming distance between two code words is defined as the number of different bit positions.

  • Let


    then the Hamming distance between

    The minimum distance decoder selects the code word "closest" in Hamming distance to the received message. A minimum distance decoder can correct m errors where m is the largest integer not to exceed


    is the minimum distance between any two valid code words.

    Example of Hamming Distances