Locally Recoverable Codes via Galois Extensions of Number Fields

• Grant number: 24/19307-3
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: September 01, 2025
• End date: August 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Herivelto Martins Borges Filho
• Grantee: Tiago Aprigio Bezerra Meireles
• Supervisor: Cecilia Salgado Guimaraes da Silva
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: University of Groningen, Netherlands
• Associated to the scholarship: 23/07508-1 - Locally recoverable codes through Galois extensions of number fields, BP.DR

Abstract

The aim of this project is to bring the constructions of Guruswami and Goldfeld et al a step further by exploring algebraic number theoretic properties of compositum of finite Galois extensions of number fields to construct locally recoverable codes with availability, i.e, locally recoverable codes, with different recovery sets. In other words, codes for which the local recoverability of a symbol can be done in more than one way.