IJPAM: Volume 70, No. 4 (2011)

EXPLICIT CONSTRUCTION OF
FINITE FIELDS USING NORMAL BASES

Anthony Y. Aidoo$^1$, Kwasi Baah-Gyamfi$^2$, Joseph Ackora-Prah$^3$
$^1$Department of Mathematics and Computer Science
Eastern Connecticut State University
Willimantic, CT 06226, USA
$^{2,3}$Department of Mathematics
Kwame Nkrumah University of Science and Technology
Kumasi, GHANA


Abstract. We present explicit methods of constructing finite fields using normal bases and develop a general rule for constructing Galois finite fields of the form $ GF(p^n) $. We also show that optimal normal basis exist for $ GF(2^n) $.

Received: February 15, 2011

AMS Subject Classification: 11T06, 12E20, 12E30, 12F10, 12Y05

Key Words and Phrases: finite fields, normal bases, irreducible polynomials

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 70
Issue: 4