Multiple of Codeword in Linear Code/Examples/V(3,3)

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