Why is d in A(n,d) not always equal to 1? In Communication Theory, for $A(n,d)$ (=the size of a largest code of
length $n$ and minimum distance at least $d$), why is $d$ not always equal to $1$?
If min. distance $= d$, for any code of length $n$, surely the min. distance is $1$, for example:
If the code is length $2$: the code words can be $01$, $11$, $00$, $10$. Here the min hamming distance between any $2$ code words is $1$.
If the code is length 3: the code words can be $000$, $001$, $010$, $100$, $011$, $101$, $110$, $111$. Again, the min hamming distance between any $2$ code words is $1$.
Can someone please explain why d isn't always just $1$?
I'm assuming my understanding of $A(n,d)$ must be wrong somehow.
Thanks!

You've interpreted "minimum distance" as a minimum over all possible codes.  The intended meaning is that each code $C$ has its own minimum distance, namely the smallest distance between any two members of $C$.  That is, the distances between pairs of distinct members of $C$ will be some set of positive integers, and the smallest of these integers is the minimum distance of $C$. 
So the intention behind $A(n,d)$ is to look at those codes $C$ for which the length  of $C$ is $n$ and the minimum distance of $C$ is $d$, and to ask how large $C$ can be. 
