Hamming Codes (6)

• Hamming codes are most easily designed by specifying the H matrix.

• For any positive integer m ³ 3, there exists an (n, k) SEC Hamming code with the following properties:

  • Code length: n = 2m - 1
  • Number of information bits: k = 2m - m - 1
  • Number of check bits: n - k = m
  • Minimum distance: dmin = 3

• The H matrix is an n ´ m matrix with all nonzero m-tuples as its column.

• A possible H matrix for a (15, 11) Hamming code, when m = 4:

(1.35)

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