Hamming codes

• An example: Construct a code that corrects a single error

  • We add m check bits to our message
    • Can encode at most (2m – 1) error positions
    • The unused (all zeros) check means no error
  • Errors can occur in the message bits and/or in the check bits
    • In n is the length of the original message then 2m – 1 >= (n + m)
  • Examples:
    • If n = 11, m = 4: 24 – 1= 15 >= (n + m) = 15
    • If n = 1013, m = 10: 210 – 1= 1023 >= (n + m) = 1023

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