Relaxed Local Correctability from Local Testing

Explore a groundbreaking lecture on relaxed locally correctable codes presented by Vinayak Kumar and Geoffrey Mon from the University of Texas at Austin. Delve into the construction of the first asymptotically good relaxed locally correctable codes with polylogarithmic query complexity, closing the superpolynomial gap between query lower and upper bounds. Discover how the innovative approach combines high-rate locally testable codes of various sizes to create a code with local testers at every scale. Learn about the process of gradually "zooming in" to desired codeword indices, where local testers at each step certify that smaller restrictions of the input have low error. Understand the significance of this method in detecting corruption and safely returning uncorrupted bits. This 37-minute talk, part of the "Advances in the Theory of Error-Correcting Codes" series at the Simons Institute, offers valuable insights into the latest developments in error-correcting code theory.