Explore the fundamentals of error-correcting codes in this graduate-level lecture from Carnegie Mellon University's "CS Theory Toolkit" course. Dive into the Hamming Code and Hadamard Code, two linear error-correcting codes with contrasting properties of rate and distance. Learn about perfect codes, Hadamard matrices, and the Schwarz Simple lemma. Gain insights from recommended resources by renowned authors in coding theory. Taught by Professor Ryan O'Donnell, this 22-minute video provides a solid foundation for research in theoretical computer science.