Topics In Normal Bases Of Finite Fields
General Mathematics
2013-04-02 v1
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.
Cite
@article{arxiv.1304.0420,
title = {Topics In Normal Bases Of Finite Fields},
author = {N. A. Carella},
journal= {arXiv preprint arXiv:1304.0420},
year = {2013}
}
Comments
172 Pages; Keywords: Finite Fields, Guassian Period, Normal Bases, Primitive Normal Bases, Primitive Polynomials