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:

\(\displaystyle 1 + 1\) \(=\) \(\displaystyle 2\)
\(\displaystyle \) \(\equiv\) \(\displaystyle 2\) \(\displaystyle \pmod 3\)


\(\displaystyle 2 + 1\) \(=\) \(\displaystyle 3\)
\(\displaystyle \) \(\equiv\) \(\displaystyle 0\) \(\displaystyle \pmod 3\)

Hence the result.

$\blacksquare$


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