Mathematical Foundations for Signal Processing, Communications, and Networking

Chapter 4    Elements of Galois Fields

Tolga M. Duman^‡

^‡ Arizona State University, Tempe, USA

This chapter deals with finite field algebra particularly useful for various channel coding and cryptography techniques. We are accustomed to operations in the field of real numbers R or rational numbers Q with the usual notions of addition, multiplication, subtraction and division. We normally do this without questioning the underlying assumptions or definitions. For the case of finite fields the operations and properties are quite different; hence, we need to go back to the basics and define these algebraic structures from the first principles.

As the material in this chapter is somewhat abstract, it may not be clear to an engineering student at a ...