Hamming Code Generator

Input

—

Hamming(7,4) Code Generator

Encode 4 data bits into a 7-bit Hamming codeword using a generator matrix G. For a message d (1×4) the codeword c (1×7) is computed as:

c = d × G  (mod 2)

Generator matrix (systematic form, 4×7):

G = [
1 0 0 0 1 1 0
0 1 0 0 1 0 1
0 0 1 0 1 0 0
0 0 0 1 0 1 1
]

Example: encode d = 1011

d = [1 0 1 1]
c = d × G (mod 2)
  = [1 0 1 1 0 0 1]
  → codeword: 1011001

Notes: All arithmetic is modulo 2 (XOR). The Hamming(7,4) code can detect and correct single-bit errors.

*** End Patch