The way David and I were able to win it in 2003: at that time, robot positions were stored as two doubles (x,y). You could move yourself by a precise amount or read the precise x,y position of another robot, each in only 1 bytecode. So instead of using broadcastMessage(String), checking that no other team was trying to screw with our messages, all of which took lots of bytecodes to get right. Instead of that, our robots communicated through the low bits of double values in their positions. Kind of like bees dancing for each other. This gave us enough of an edge to beat out all the other players. This was 100% David Greenspan's idea, by the way. I just worked hard to help code it up.
MIT classes are supposedly a lot of hard work, but at that point I had never worked as hard on anything as I did on our BattleCode player.