Explicit Factorization of Generalized Cyclotomic Polynomials of Order $2^m 3$ Over a Finite Field $F_q$

We give explicit factorizations of $a$-cyclotomic polynomials of order 2^m 3, Q_2^m3,a(x), over a finite field F_q with $q$ elements where $q$ is a prime power, $m$ is a nonnegative integer and $a$ is a nonnegative element of F_q. We use the relation between usual cyclotomic polynomials and $a$-cyclotomic polynomials. Factorizations split into eight categories according to $q \equiv \pm1$ (mod 4), $a$ and $-3$ are square in F_q. We find that the coefficients of irreducible factors are primitive roots of unity and in some cases that are related with Dickson polynomials.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Campus Only Dissertation

Discipline thesis:degree_discipline

Mathematics

Year dc:date.available

2013

Author dc:creator

• Tosun, Cemile

Contributors dc:contributor

• Fitzgerald, Robert

• Cyclotomic Polynomials
• Dickson Polynomials
• Factorization
• Finite Field

Repository record dc:identifier

https://opensiuc.lib.siu.edu/dissertations/733

OAI identifier oai:identifier

oai:opensiuc.lib.siu.edu:dissertations-1736