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Explore the fundamentals of coding theory in this lecture delivered by Mrinal Kumar as part of the ICTS Workshop on High Dimensional Expanders and Codes. Delve into advanced concepts in error-correcting codes, which form the backbone of modern communication systems by enabling reliable data transmission in the presence of noise. Learn about the mathematical foundations and theoretical principles that underpin coding theory, including recent breakthroughs in list-decodable and locally decodable/testable codes. Examine the intersection between coding theory and high dimensional expansion, two rapidly evolving fields in computer science and mathematics. Gain insights into how these concepts apply to both classical and quantum LDPC codes, and understand their significance in theoretical computer science, mathematics, and electrical engineering. This lecture is part of a comprehensive program that brings together leading researchers to discuss cutting-edge developments in error-correcting codes and their applications in various computational and communication contexts.
