1. Input Message (4 bits)
Message:
2. Codeword (7 bits)
Click a bit to flip it (simulate error)
Parity Check Matrix H
Syndrome s = H·c (mod 2)
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Error Location
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Hamming Bound
Try Different Codes
Hamming(7,4): 4 data bits + 3 parity bits = 7-bit codeword. Minimum distance d=3 → correct 1 error.
Syndrome s=H·c(mod2) gives binary address of the error. The Hamming bound: 2^(n-k) ≥ C(n,0)+C(n,1) = 1+n.
Perfect codes meet this bound exactly. Hamming(7,4) is perfect: 2³=8=1+7. ✓