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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 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 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 capacity-achieving results. Understand how coding theory intersects with high dimensional expansion, a relatively new area of interest spanning mathematics and theoretical computer science. Gain insights into the mathematical principles that help solve communication challenges in both random and adversarial noise environments, building upon seven decades of research in mathematics, theoretical computer science, and electrical engineering. This lecture forms part of a comprehensive program organized by leading experts from The Weizmann Institute, UC Berkeley, and TIFR Mumbai, designed to bridge the gap between high dimensional expanders and error-correcting codes.
