Speaker
Description
Goppa codes form a structured family of linear error-correcting codes introduced by Valery D. Goppa in 1970 and later interpreted within the framework of algebraic geometry as codes arising from algebraic curves over finite fields. Binary Goppa codes with irreducible Goppa polynomials are used in the Classic McEliece post-quantum key encapsulation mechanism (PQ-KEM), where their efficient decoding algorithms and resistance to structural attacks underpin a long-standing and well-studied code-based public-key encryption scheme.
Motivated by classical Goppa codes, multivariate Goppa codes are an analogous family of codes constructed using multivariate polynomials, originally introduced by Hiram H. López and Gretchen L. Matthews in 2021. In this talk, we generalize the original construction and show that these generalized multivariate Goppa codes exhibit similar rank and distance bounds, as well as comparable structural properties. We conclude by discussing their connection to classical Goppa codes and their suitability for cryptographic applications.