Let $\mathcal{A}$ be a finite alphabet. Explain what is meant by saying that a binary code $c: \mathcal{A} \rightarrow\{0,1\}^{*}$ has minimum distance $\delta$. If $c$ is such a binary code with minimum distance $\delta$, show that $c$ is $\delta-1$ error-detecting and $\left\lfloor\frac{1}{2}(\delta-1)\right\rfloor$ error-correcting.

Show that it is possible to construct a code that has minimum distance $\delta$ for any integer $\delta>0$.