Finite Fields: Algebraic Structures and Coding Applications

This lecture covers the fundamental concepts of finite fields, including their definition, properties, and applications in coding theory. It explains the structure of finite fields, the field axioms, and the characteristic of a finite field. The lecture also delves into examples of calculations over finite fields, such as solving equations and performing linear algebra operations. Additionally, it explores the usefulness of finite fields in algebraic manipulations and highlights the isomorphism between finite fields and other algebraic structures.