Exploring Finite Fields and their Applications in Coding Theory

Abstract

Finite fields, also known as Galois fields, are fundamental algebraic structures with applications in various areas of mathematics and computer science. This paper will delve into the properties of finite fields and explore their applications in coding theory, a branch of mathematics concerned with designing and analyzing error-correcting codes. We will discuss how finite fields are used to construct error-correcting codes that can detect and correct errors that may occur during data transmission or storage.