O'Reilly logo

Elements of Algebraic Coding Systems by Valdemar Cardoso da Rocha, Jr.

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

Chapter 5

IRREDUCIBLE POLYNOMIALS OVER FINITE FIELDS

5.1 Introduction

The theory of finite fields constitutes a very important tool in many practical situations. In particular, it is worth mentioning its use in algebraic coding and cryptography. As we have already seen, the construction of cyclic codes relies on knowledge of irreducible polynomials over finite fields. Similarly, modern cryptographic systems also rely on the structure of finite fields, e.g., the Advanced Encryption Standard (Daemen and Rijmen 2002).

Polynomials are important in the study of the algebraic structure of finite fields and irreducible polynomials are the prime elements of the polynomial ring over a finite field. Irreducible polynomials are indispensable for constructing ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required