IJPAM: Volume 115, No. 3 (2017)

Title

A NOTE ON CONSTRUCTION OF IRREDUCIBLE
POLYNOMIALS OVER FINITE FIELDS
WITH CHARACTERISTIC 2

Authors

Murat Alan$^1$, Betül Duman$^2$
$^{1,2}$Mathematics Department
Faculty of Arts and Sciences
Yildiz Technical University
Davutpasa Campus, 34210, Esenler, Istanbul, TURKEY

Abstract

Let $f(x)$ be an irreducible polynomial of degree $m$ over the finite field $\mathbb F_{q}$ where $q$ is a power of 2. We show that the polynomial $x^{2m}f\left( \frac{x^4+x^3+x+1}{x^2} \right)$ is an irreducible polynomial of degree $4m$ over $\mathbb F_{q}$ under some conditions on coefficients of $f(x).$

History

Received: March 10, 2017
Revised: May 30, 2017
Published: July 27, 2017

AMS Classification, Key Words

AMS Subject Classification: 11C08, 12E05, 12E20
Key Words and Phrases: finite fields, irreducible polynomials, composition of polynomials

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Bibliography

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How to Cite?

DOI: 10.12732/ijpam.v115i3.6 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 115
Issue: 3
Pages: 529 - 532


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