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Explore advanced concepts in coding theory through this lecture delivered by Swastik Kopparty as part of the ICTS Workshop on High Dimensional Expanders and Codes. Delve into the mathematical foundations and theoretical frameworks that underpin error-correcting codes, which form the backbone of modern communication systems by enabling reliable data transmission in the presence of noise. Learn about the intersection between coding theory and high dimensional expansion, two rapidly evolving fields in computer science and mathematics that have experienced significant breakthroughs in recent years. Examine how these concepts relate to list-decodable and locally decodable/testable codes, polar codes, and quantum LDPC codes. Gain insights into the mathematical structures and algorithms that enable robust communication systems capable of handling both random and adversarial errors. This lecture forms part of a comprehensive program exploring the connections between high dimensional expanders and error-correcting codes, designed for graduate students and researchers in computer science, mathematics, and electrical engineering.
