Table of Contents
Algebra
Volume 2014, Article ID 482837, 7 pages
http://dx.doi.org/10.1155/2014/482837
Research Article

The Reducibility of a Special Binary Pentanomial

1Faculty of Mathematics, Kim Il Sung University, Pyongyang, Democratic People’s Republic of Korea
2Department of Applied Mathematics, Kim Chaek University of Technology, Pyongyang, Democratic People’s Republic of Korea

Received 30 May 2014; Accepted 20 August 2014; Published 2 September 2014

Academic Editor: Peter Fleischmann

Copyright © 2014 Ryul Kim and Yun Mi Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Swan’s theorem determines the parity of the number of irreducible factors of a binary trinomial. In this work, we study the parity of the number of irreducible factors for a special binary pentanomial with even degree , where , and exactly one of  ,  and   is odd. This kind of irreducible pentanomials can be used for a fast implementation of trace and square root computations in finite fields of characteristic 2.