This is not error correction issue though. Error correction means taking known data and adding redundancy to it so that damaed pieces can be repaired. This makes the message longer.

An llm’s output does not contain error correction. It’s just the output. And it doesn’t contain any errors, mathematically speaking. The hallucination is the correct output. It is what the statistics it gathered from its training set determined is most likely. A “correct” llm output is indistinguishable from a “hallucination”, mathematically, and always will be. A hallucination is simply “some output that some human, somewhere, doesn’t like”, and that’s uncomputable. And outputs that people subjectively consider as “hallucinations” cannot be eliminated, because an llm is, fundamentally, a probabilistic algorithm. If you added error correction to an llm’s output all you’d be able to recover is the llm’s original output, “hallucinations” and all.

Tldr: “hallucinations” are a subjective thing. A Hallucination" is not an error that can be corrected after-the-fact, because it is not an error in the first place.