Which mathematical invention has had the most impact over the last 50 years? An error-correcting code would be a strong contender. Error-correcting codes protect digital information, which is being transmitted or stored, from random errors. Coding Theory looks at how such codes work and how to improve them. This course should convince you that the most fundamental objects from "pure" maths - matrices, binomial coefficients, the binomial distribution, primes, polynomials, groups, finite fields, projective spaces, even the Pigeonhole Principle and truth tables - have compelling practical applications, because they are all used in design and analysis of error-correcting codes. Without Coding Theory, modern digital communication (as we know it) would not exist. Two error-correcting codes, H8 due to Hamming and G24 due to Golay, are directly linked to the 2022 Fields Medal-winning work on densest sphere packings in dimensions 8 and 24 by Viazovska.
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