A Near-Cubic Lower Bound for 3-Query Locally Decodable Codes from Semirandom CSP Refutation — mentioned by foota

Wed, 10 Jan 2024 20:21:52 GMT

I think there's a few areas of improvement. One is for yet better three query locally decodable codes (like I said, I think it's still not (sub)linear in space, which is likely a blocker for real use), another is for larger constants, and then as you note, for non-constant queries. My impression though is that the more interesting question is for larger constants (e.g., four query, etc.,). edit: interestingly, it looks like an earlier paper from overlapping authors proves a lower bound of k^3 (where k is the original message's length) for 3 query locally decodable codes…

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A Near-Cubic Lower Bound for 3-Query Locally Decodable Codes from Semirandom CSP Refutation · HackerPapers discussions

A Near-Cubic Lower Bound for 3-Query Locally Decodable Codes from Semirandom CSP Refutation — mentioned by foota