Solution
= Solution
Delete any $d-1$ coordinates. The resulting puncturing map
$$
\pi:C\longrightarrow\mathbb F_2^{n-d+1}
$$
is injective: if $\pi(x)=\pi(y)$ for distinct codewords, then the nonzero codeword $x-y$ is supported on at most $d-1$ coordinates, contradicting the minimum distance. Thus
$$
2^k=|C|\leq2^{n-d+1},
$$
which is the <Singleton bound>
$$
\boxed{n\geq d+k-1}.
$$