A construction of LRC Codes on Function Field Towers

GALLUCCIO FRANCISCO

Rio de Janeiro

Seminario; Student Algebraic Geometry and Foliations Seminar at IMPA; 2022

Instituto de Matemática Pura e Aplicada

Locally Recoverable Codes (LRC Codes) were developed in the last years as a solution for distributed storage as the recovery of any erased coordinates using only a small fraction of the codeword. The most recent constructions came from Algebraic-Geometric Codes, in particular from coverings of curves and fiber product of curves. In this talk we will talk about Function Fields, and trying to adapt these constructions to this category, and describing a way to generalize the construction to some Towers of Function Fields. In particular, we will show an example using the Garcia-Stichtenoth Tower to see the properties of this construction