$A(n,d)$ is the size of a largest code of length $n$ and minimum distance at least $d$. (Im using Hamming distance as my distance)
Im trying to show from first principles that $A(4,3)=2$
Its easy to show $A(4,3)\geq 2$, just give a code of size 2 that has length $n$ and min.dist $\geq 3$
So I need to argue that $A(4,3)\leq 2$ and this can be done by showing that there is no code of size 3 satisfying the conditions. I can see why this is a case but Im struggling to write a neat argument which proves a code with length $4$ and min distance $3$ can't have size $3$.