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Coding of Hamming
Principle de Decoding
Sent message : 1100110
Received message : 1100100
Example :The check of the bit 1 is correct, the sum is very even.
The check of the bit 2 is false, the sum is odd.
The check of the bit 4 is false, the sum is so odd there.
To know the number of the erroneous bit, we add every bit of parity which has no wished parity. Here the bits 2 and 4. Thus 2 more 4 give 6, there is an error on the bit 6. The new message becomes:
Corrected successful message : 1100110
It does not more remain than to unpacked the successful coded message. At the end we obtain 0110. The message was well corrected. If we had had several errors in the message, the number of erroneous bit will be bigger than the number of successful bits. We can deduct from this last example that the coding can correct an error, and can discover some error but without possible correction.
