Multiple of Codeword in Linear Code/Examples/V(3,3)
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Example of Multiple of Codeword in $V \paren {3, 3}$
In the master code $V \paren {3, 3}$, the codeword $102$ is multiplied by $\eqclass 2 3$ thus:
- $2 \paren {102} = 201$
Proof
Taking the elements of $201$ in turn, we have:
\(\ds 2 \times 1\) | \(=\) | \(\ds 2\) | ||||||||||||
\(\ds \) | \(\equiv\) | \(\ds 2\) | \(\ds \pmod 3\) |
\(\ds 2 \times 0\) | \(=\) | \(\ds 0\) | ||||||||||||
\(\ds \) | \(\equiv\) | \(\ds 0\) | \(\ds \pmod 3\) |
\(\ds 2 \times 2\) | \(=\) | \(\ds 4\) | ||||||||||||
\(\ds \) | \(\equiv\) | \(\ds 1\) | \(\ds \pmod 3\) |
Hence the result.
$\blacksquare$
Sources
- 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): Chapter $6$: Error-correcting codes