For any value of $q$ the largest number of elements in any q-ary code $C$ of length $4$, distance $3$ is $q^2$. How can we prove that this is attainable iff there are a pair of mutually orthogonal latin squares of order $q$?
Please show the full proof if you can. I am looking for the proof in order to proceed with my study of the subject. This is not to say I have not attempted to approach the problem- I just haven't the slightest idea how to.
If you could please be explicit in your explanation.
See if you can figure it out from pages 23 and 24 of these notes. It's also proved as Theorem VI.3.2 of these notes.