Note: A Hamming code satisfies the relation 2^{m} ≥ n+1, where n is the total number of bits in the block, k is the number of information bits in the block, and m is the number of check bits in the block, where m = n k .
The Hamming code is computed as follows:
To decode it:
E.g. To encode '01111101000' where the MSB is written first:
0111110x100x0xxx 011111011000001x (the x is bit 0 which is ignored)Transmit it with an error:
011101011000001Compute parities:
0111010110000010 01110101 1 0111 1000 0 01 01 10 00 1 0 1 0 0 1 0 0 1 1Bit 11 (1011 in binary) is in error. Flip it:
0111110110000010Extract the data:
0111110 100 0(Bit 0 was appended to the received data so that if there were no errors, we could flip it.)
Other variants of Hamming code are in use; they are rearrangements of the bits so that the parity bits are at the end.
Source: from Federal Standard 1037C
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