get on your knees and thank me wrote:

You made me check Memory Alpha, you goddamn son of a bitch.

The prefix code was a numbered code individually assigned to each Federation starship. It was a defensive measure designed to help Starfleet personnel combat enemies who had seized control of a ship of their fleet, and to prevent enemy ships from attempting to seize control of a Starfleet vessel.

When the relevant code was entered into the computer system of another ship, that ship was able to remotely control systems on the other ship. This included weapons and defense systems, which enabled the controlling ship to reduce the seized ship's fighting capabilities in order to permit effective attacks. However, a knowledgeable enemy could take the precaution of changing the code.

That's it. That's all the info on it from Star Trek's very own version of Wookiepedia, straight from the beardiest of beardos.

So it was a dumb plot point they came up with that doesn't hold up to 2 seconds of scrutiny, just like the "we knew it could emit catastrophic radiation leaks so we built a shield around it, but never thought to install any means to repair said leaks, short of unprotected suicide bodies" engine warp thingy. Weak points in an otherwise good movie.

If you're going to dig into some Starfleet technical manual to rebut, don't bother, because then I'll have won twice (??_?)