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 6

FINITE FIELD FACTORIZATION OF POLYNOMIALS

6.1 Introduction

The development and design of many practical applications involving digital sequences require the factorization of polynomials. In particular, a cyclic code or a similar mathematical structure requires the factorization of xn + 1 as a product of irreducible polynomials with roots in a finite field, where n denotes a positive integer. The global positioning system (Parkinson and Spilker Jr. 1996, pp.114-118) and digital video broadcast (Alencar 2009, pp.89–93) are just two examples where the factorization of polynomials in finite fields is employed.

Let again the factorization derived in Theorem 5.4 be considered, i.e.,

In (6.1) Vd(x) denotes the product of all monic irreducible ...

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