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Explore a 42-minute lecture on asymptotically-good relaxed locally correctable codes (RLCCs) with (log n)^{2+o(1)} queries, presented by Tal Yankovitz from the Weizmann Institute of Science at the Simons Institute. Delve into recent advancements in error-correcting codes, focusing on the significant milestone achieved by Kumar and Mon in constructing asymptotically good RLCCs with poly-logarithmic query complexity. Examine the intriguing question of determining the optimal value of e between 0.5 and 69 for which asymptotically-good RLCCs with query complexity (log n)^{e+o(1)} exist. Learn about the substantial progress made in narrowing this gap through the development of asymptotically-good RLCCs with a query complexity of (log n)^{2+o(1)}. Understand the key insight driving this work, which involves recognizing that strong local testability guarantees exceed the requirements for the Kumar-Mon reduction. Discover how replacing locally testable codes (LTCs) with "vanilla" expander codes possessing local testability properties near the code leads to improved results. This lecture is part of the "Advances in the Theory of Error-Correcting Codes" series and is based on joint work with Gil Cohen.
