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Explore advanced concepts in coding theory through this lecture delivered by Mrinal Kumar as part of the ICTS Workshop on High Dimensional Expanders and Codes. Delve into the mathematical foundations and theoretical aspects of error-correcting codes, which form the backbone of modern communication systems by enabling reliable data transmission in the presence of noise. Learn about the latest developments in this field that has experienced significant breakthroughs in recent years, including new list-decodable and locally decodable/testable codes, polar codes, and quantum LDPC codes. Examine the intersection between coding theory and high dimensional expanders, two rapidly evolving areas in computer science and mathematics. Gain insights into how these mathematical structures contribute to solving fundamental problems in theoretical computer science and electrical engineering, building upon seven decades of research while incorporating cutting-edge advances that have emerged in the contemporary landscape of information theory and combinatorics.
