Multivariate Goppa Codes - Applications in Cryptography and Error Correction

Explore the world of multivariate Goppa codes in this 51-minute seminar presented by Gretchen Matthews from Virginia Tech. Delve into the evolution of Goppa codes, from their introduction in 1971 using univariate polynomials to the modern multivariate approach. Discover how the properties of these codes are intrinsically linked to their generator polynomials and their significance in the McEliece cryptosystem. Gain insights into various perspectives on Goppa codes and understand their capabilities. Learn about the extension to multivariate Goppa codes, their parameters, and dual codes. Explore the applications of these codes in entanglement-assisted quantum error correction and in constructing long LCD, self-dual, or self-orthogonal codes. This seminar, part of the Society for Industrial and Applied Mathematics' SAGA series, offers a comprehensive look at cutting-edge research in applied geometry and algebra.