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Consider now the new non - standard Hamming ( 7 , 4 ) code that uses encoding matrix H = 1 1 0 0 1
Consider now the new nonstandard Hamming code that uses encoding matrix
H
and produces an encoded message with check digits at positions
and
When the encoding matrix is not the standard one, the message is encoded differently, though it is still done in such a way that HxT
over Z
for any encoded message x
We can find the encoding of a message abcd
by setting x
axyzbcd
and evaluating HxT
deducing the values of xyz
needed to ensure HxT
over Z
When the positions of the check digits correspond with the positions of the basis vectors in the encoding matrix, finding the encoding is fairly straightforward.
The decoding method is exactly the same as before, though we should again be careful to ignore the check digits when extracting the original message.
c
Using the Hamming code described above, encode the message
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