What does it mean to say a binary code $C$ has length $n$, size $m$ and minimum distance d?

Let $A(n, d)$ be the largest value of $m$ for which there exists an $[n, m, d]$-code. Prove that

$$\frac{2^{n}}{V(n, d-1)} \leqslant A(n, d) \leqslant \frac{2^{n}}{V(n,\lfloor(d-1) / 2\rfloor)}$$

where

$$V(n, r)=\sum_{j=0}^{r}\left(\begin{array}{l} n \\ j \end{array}\right)$$

Another bound for $A(n, d)$ is the Singleton bound given by

$$A(n, d) \leqslant 2^{n-d+1}$$

Prove the Singleton bound and give an example of a linear code of length $n>1$ that satisfies $A(n, d)=2^{n-d+1}$.