3.13 Hamming Code
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
Example:<br />
Consider the 2 nd -order RM code for m=4,<br />
n = 2<br />
4 =<br />
16<br />
⎛4⎞<br />
⎛4⎞<br />
k = 1 + ⎜ ⎟ + ⎜ ⎟ = 11<br />
⎝ 1⎠<br />
⎝ 2⎠<br />
n - k = 16 - 11 = 5<br />
d<br />
= 2<br />
2<br />
min<br />
=<br />
4<br />
This is a (16, 11) linear code.<br />
The generator matrix is given by<br />
G<br />
R(<br />
2, 4)<br />
⎡ v0<br />
⎢<br />
v<br />
⎢<br />
4<br />
⎢ v3<br />
⎢<br />
⎢<br />
v2<br />
⎢ v1<br />
⎢<br />
= ⎢v4v<br />
⎢v4v<br />
⎢<br />
⎢v4v<br />
⎢v3v<br />
⎢<br />
⎢v3v<br />
⎢<br />
⎣v2v<br />
3<br />
2<br />
1<br />
2<br />
1<br />
1<br />
⎤<br />
⎥<br />
⎥<br />
⎥<br />
⎥<br />
⎥<br />
⎥<br />
⎥<br />
⎥<br />
⎥<br />
⎥<br />
⎥<br />
⎥<br />
⎥<br />
⎥<br />
⎥<br />
⎦
Change language