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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, building upon previous lectures in this comprehensive series. Examine 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. Learn how error-correcting codes enable reliable communication in noisy environments and discover their applications across mathematics, theoretical computer science, and electrical engineering. Gain insights into the latest developments in list-decodable codes, locally decodable and testable codes, polar codes, and quantum LDPC codes that have emerged from seven decades of active research. Understand the connections between expander graphs and their higher-dimensional generalizations to hypergraphs and simplicial complexes, and how these concepts relate to coding theory applications.
