Addition of Codewords in Linear Code/Examples/V(2,3)

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