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

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Chapter 8

LINEARIZED POLYNOMIALS

8.1 Introduction

Linearized polynomials are useful in the study of polynomial factorization techniques because they have enough structure to allow an easy procedure to find their roots.

DEFINITION 8.1 Over GF(qm), a linearized polynomial (or a q-poly- nomial) is defined as a polynomial of the form

with coefficients in the extension field GF(qm) of GF(q).

8.2 Properties of L(x)

Let F be an arbitrary extension of GF(qm).

THEOREM 8.2 Let , then it follows that

(a) Property 1:

(b) Property 2:

Proof:

Property 1.

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