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Explore advanced concepts in coding theory through this fifth 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 intricate relationships between coding theory and high dimensional expansion, two rapidly evolving fields that have experienced significant breakthroughs in recent years. Learn how error-correcting codes serve as the backbone of modern communication systems, enabling reliable data transmission in the presence of both random and adversarial noise. Discover the latest developments in list-decodable and locally decodable/testable codes, polar codes, capacity-achieving results, and quantum LDPC codes that have emerged from seven decades of active research in mathematics, theoretical computer science, and electrical engineering. Gain insights into the intersection of these two mathematical areas through expert instruction designed for graduate students and postdoctoral researchers working in computer science, mathematics, or electrical engineering.
