Locally Testable Codes with Constant Rate, Distance, and Locality

Explore a groundbreaking lecture on locally testable codes with constant rate, distance, and locality presented by Irit Dinur from the Weizmann Institute of Science. Delve into the history and fundamentals of local testable codes, high-dimensional expander codes, and their applications. Examine the main results, including expander codes, Tanner codes, and situation codes. Understand the intricacies of defining expander codes, complex squares, and code words. Investigate local views as tensor codes and the proof of local testability in this comprehensive 67-minute talk from the Simons Institute's Breakthroughs series.

Introduction
Local Testable Codes
History of Local Testable Codes
Local Checkers
HighDimensional Expanders Codes
Main Result
Expander Codes
Tanner Codes
Situation Codes
Defining Expander Codes
Defining Complex
Squares
Square Complex
Code
Code Words
Local Views
Local Views as Tensor Codes
Local Testability Proof