Parity extension
= Parity extension
Appending a parity bit makes every word even-weight. A binary $[n,m,d]$ code becomes an $[n+1,m,d^+]$ code, where
$$
d^+=
\begin{cases}
d,&d\text{ even},\\
d+1,&d\text{ odd}.
\end{cases}
$$
= Parity extension
Appending a parity bit makes every word even-weight. A binary $[n,m,d]$ code becomes an $[n+1,m,d^+]$ code, where
$$
d^+=
\begin{cases}
d,&d\text{ even},\\
d+1,&d\text{ odd}.
\end{cases}
$$