To expand on the title: When I publish my game on GitHub, and the voting ends, can I add patches or updates to the game? I didn't find anything about that in the rules.

It is common for jam entries to be judged on the state they're in at the time of the deadline. After the judgement there's nothing stopping you from developing your game further.

Even during the voting it should be ok to develop your game further, btw. As long as you do so in a seperate branch without modifying any of the binaries (executables) on your project page. As long as judging is in progress people should (be able to) judge the game based on the version of the moment of the deadline.

Of course you are also expected to try and judge the results of the other contestants during this time.

During the voting period only bug fixes are ok,  especially bugs that make your game unplayable.  Major game play changes or extra polish are not ok during the voting period.  Or you could create a fork call post-jam,  so people know now to rate that.   Like LucKey said,  after voting is over your're free to do whatever you want with your game.