= Solution
A <binary block code> of length $n$ is a subset $C\subseteq\mathbb F_2^n$. Its size is $M=|C|$, and its minimum <Hamming distance> is
$$
d=\min_{\substack{x,y\in C\\x\ne y}}d_H(x,y).
$$
Thus an $[n,M,d]$ code consists of $M$ binary words of length $n$ whose distinct pairs differ in at least $d$ coordinates. When $d=1$, every set of distinct words qualifies. Taking all of the <vector space over a finite field>[binary vector space] $\mathbb F_2^n$ gives $2^n$ words, and no code can contain more words than its ambient space. Hence
$$
\boxed{A(n,1)=2^n}.
$$
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