Re: "I don't fully understand the correspondence between the paper and the code"

Have you tried contacting the paper's author(s)? Preferably the PhD student that did the actual work?

I used to do that when I couldn't make sense of a paper. Not all authors will respond, some might brush you off with a generic remark to read the appendix or whatever. But it's worth a try. In one case, the author frankly told me that the code didn't work as well as it sounded in the paper -- the algorithm was so instable that it wasn't very useful. But they couldn't have written that in the paper, or it might not have been accepted.