Date of Award

January 2015

Degree Type

Open Access Thesis

Degree Name

Master of Science (MS)

Department

Mathematics and Statistics

First Advisor

Patrick J. Costello

Department Affiliation

Mathematics and Statistics

Second Advisor

Bangteng Xu

Department Affiliation

Mathematics and Statistics

Third Advisor

Rachel Bishop-Ross

Department Affiliation

Mathematics and Statistics

Abstract

In this paper, we generate algorithms for factoring polynomials with coefficients in finite fields. In particular, we develop one deterministic algorithm due to Elwyn Berlekamp and one probabilistic algorithm due to David Cantor and Hans Zassenhaus. While some authors present versions of the algorithms that can only factor polynomials of a certain form, the algorithms we give are able to factor any polynomial over any finite field. Hence, the algorithms we give are the most general algorithms available for this factorization problem. After formulating the algorithms, we look at various ways they can be applied to more specialized inquiries. For example, we use the algorithms to develop two tests for irreducibility and a process for finding the roots of a polynomial over a finite field. We conclude our work by considering how the Berlekamp and Cantor-Zassenhaus methods can be combined to develop a more efficient factoring process.

Included in

Mathematics Commons

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