3.13 Hamming Code
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The codewords are given by<br />
c<br />
= d ⋅G<br />
Example: r=1, m=3<br />
c = ( c c1<br />
Lc7<br />
) = ( d0<br />
d3<br />
d2<br />
d1<br />
0<br />
)<br />
⎡1<br />
⎢<br />
0<br />
⎢<br />
⎢0<br />
⎢<br />
⎣0<br />
1<br />
0<br />
0<br />
1<br />
1<br />
0<br />
1<br />
0<br />
1<br />
0<br />
1<br />
1<br />
1<br />
1<br />
0<br />
0<br />
1<br />
1<br />
0<br />
1<br />
1⎤<br />
1<br />
⎥<br />
⎥<br />
1⎥<br />
⎥<br />
0⎦
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