Addition of Codewords in Linear Code/Examples/V(2,3)
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Example of Addition of Codewords in $V \paren {2, 3}$
In the master code $V \paren {2, 3}$, the codewords $12$ and $11$ are added thus:
- $12 + 11 = 20$
Proof
Taking the elements of $12$ and $11$ in pairs, successively, we have:
\(\ds 1 + 1\) | \(=\) | \(\ds 2\) | ||||||||||||
\(\ds \) | \(\equiv\) | \(\ds 2\) | \(\ds \pmod 3\) |
\(\ds 2 + 1\) | \(=\) | \(\ds 3\) | ||||||||||||
\(\ds \) | \(\equiv\) | \(\ds 0\) | \(\ds \pmod 3\) |
Hence the result.
$\blacksquare$
Sources
- 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): Chapter $6$: Error-correcting codes