Topics In Normal Bases Of Finite Fields

2013/04/01 by N. A. Carella, Carella, N. A.
Computer Science · #11T06 #11T30 #Cellular Automata and Applications #Coding theory and cryptography #Cryptographic Implementations and Security #FOS: Mathematics #General Mathematics (math.GM)

paper · pdf · doi:10.48550/arxiv.1304.0420

openalex publication_date 2013/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is an introduction to the theory of normal bases of finite fields. The first few chapters cover a wide range of topics on the theory of normal bases of finite fields. Most standard definitions and results, including proofs are given. The last few chapters cover the theory of guassian and period normal bases of finite fields of low degrees. The last chapter presents the asymptotic proofs of the existence of primitive polynomials of degree n with approximately n/2 arbitrary coefficients, and primitive normal polynomials of arbitrary traces.

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• On the Coefficients of Primitive Normal polynomials
• Variations of the Primitive Normal Basis Theorem
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