Hamming code errors DETECTION only..

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nego

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Hi all,

I have a message with 10011010100 which gives me a (15,11) hamming code of 100110100101011. However, the transmitted code is 101110000101011,where two errors are exist. Now i need to DETECT the errors but not correct them. Is there any method for detecting the double error in the code??? Can anyone help??
 

Hi Nego

Linear block codes can be represented as

\[c=mG\]

where \[ G \] is the generator matrix. Another way to characterize codes is by the 'parity check matrix' which is the matrix of basis of codes orthogonal to the codes \[c=mG\] i.e.
\[cH^T=0\]

Just multiply the receive code word by \[H^T\]. If the result is non-zero then it means there is at least one bit in error. In hamming codes, the minimum distance of code is 3, so this scheme can detect errors of at most \[2=d_{min}-1\] bits.

Hope this helps.
 

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