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Explore the construction of locally testable codes with multiplication properties derived from high-dimensional expanders in this 36-minute conference talk. Delve into the intersection of high-dimensional expansion theory and error-correcting codes, examining how HDXs can be leveraged to create codes with specific algebraic properties. Learn about the theoretical foundations connecting expander graphs to higher-dimensional structures and their applications in coding theory. Understand the significance of locally testable codes in computational complexity and their role in probabilistically checkable proofs. Discover how the multiplication property enhances the utility of these codes for various applications in theoretical computer science. Gain insights into recent developments in this rapidly evolving field that bridges combinatorics, algebra, and computer science, presented as part of the ICTS Workshop on HDXs and Codes focusing on cutting-edge research in high-dimensional expanders and error-correcting codes.
