So I'd been thinking about something fancy like Shamir's secret sharing or some other threshold scheme, but actually, an xor check word is still really good - not only does it check, but if you know that only a single word was wrong and which it was, it can recover that word, or if you don't know which word but are confident it was only one, then you can narrow it down to just 4 possible locations, which will probably be good enough to identify the actual location most of the time.