I understand what the covering radius is, I know the definition and I can manually work it out if need be. I don't mind working it manually when $n=2$ or $n=3$ but I have been faced with questions where $n=8$; writing out $(F_2)^8$ or the even more dreadful $(F_3)^8$ is far too long of a process?
Surely there is a more efficient way? or an intuitive way to get around this?
In all solutions to large $(F_q)^n$ the study material I'm using has used some magical intuiton to say "no codeword will be more than 4 symbols away from..." and gone on to conclude that the covering radius is 4 etc. and that doesn't teach a method to approach an unseen scenario but rather only solves the one at hand.
I prefer deeper understanding of what is happening and how to approach any scenario rather than knowing how to deal with certain scenarios!
Thanks in advance!