Introduction to finite fields and to algebraic error-correcting codes

• Grant number: 21/13390-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: March 01, 2022
• End date: December 31, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Robson Ricardo de Araujo
• Grantee: Natan Santana de Vasconcelos
• Host Institution: Instituto Federal de Educação, Ciência e Tecnologia de São Paulo (IFSP). Campus Cubatão. Cubatão , SP, Brazil

Abstract

This work consists of a study, at the scientific initiation level, on basic aspects of finite field theory and its applications to algebraic error-correcting codes, with emphasis on linear codes. In particular, this project proposes a study on cyclic codes, BCH codes, Reed-Solomon codes, and LDPC codes. (AU)