= Solution
For a <binary block code>, $n$ is the common length of its codewords, $m=|C|$ is the number of codewords, and
$$
d=\min_{\substack{x,y\in C\\x\ne y}}d_H(x,y)
$$
is its minimum <Hamming distance>.
The <parity extension> is
$$
C^+=\left\{
\left(x_1,\ldots,x_n,\sum_{j=1}^nx_j\right):x\in C
\right\}.
$$
Every extended word has even <Hamming weight>. The distance between two words increases by one exactly when their original distance is odd, so
$$
\boxed{
C^+\text{ has parameters }[n+1,m,d^+],
\qquad
d^+=
\begin{cases}
d,&d\text{ even},\\
d+1,&d\text{ odd}.
\end{cases}}
$$
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