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Hamming Distance:

Hamming Code:

Humming code is 1-bit Error Correcting Code.

Let consider we send m bit manage transmitted to receive for error-correcting or detecting we add an extra parity bit(s).

# So, when m + p bits transmitted to the receiver how many cases will occur.

1)  There is no error.

2)  1-bit error either at m bit or at p bit.

So, any one of them corrupted – m + p

No error is there – 1

Now we should able to detect each one of the cases separately using p bit(s).

Important point:

Let’s take an example:

Now, how can we handle the cases over p parity bit (s)?

According to this condition, we decide how bits require for parity bit to add at the original message (m): 

Definitely more than 3 bit is also possible but we always choose as small a bit as possible as parity bit which satisfies the condition.

So, for error correction, we should add 3 bits as parity with the original message (4 bits) then 4 + 3 (bits) = 7 bits we are sending.

So, when we send 7 bits how many cases occur. So, error may present at bit number (1 or 2 or 3 or 4 or 5 or 6 or 7, 0 (no error))

So, 8 cases are possible.