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Learn about error-correcting codes and their theoretical foundations in this Computer Science and Discrete Mathematics seminar presented by Shashank Srivastava from the Institute for Advanced Study. Explore how spectral expanders can be used to construct explicit list decoding capacity achieving codes that approach the generalized Singleton bound without relying on algebraic methods. Discover the evolution of error-correcting codes from practical communication tools to fundamental objects in theoretical computer science, with connections to complexity theory and pseudorandomness. Examine the groundbreaking approach that achieves optimal list sizes over constant sized alphabets using a distance amplification scheme, marking the first explicit family of codes to do so. Understand the local-to-global phenomenon for the generalized Singleton bound and learn how this construction supports properties like LDPC and linear time unique decodability, all through the lens of combinatorial properties in expander graphs. The research presented is a collaborative effort with Fernando Granha Jeronimo, Tushant Mittal, and Madhur Tulsiani.
