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Journal of Mathematics
Volume 2014, Article ID 258187, 7 pages
http://dx.doi.org/10.1155/2014/258187
Research Article

Self-Dual Normal Basis of a Galois Ring

Algebra Research Group, Institut Teknologi Bandung, Bandung 40132, Indonesia

Received 12 May 2014; Revised 13 August 2014; Accepted 15 August 2014; Published 1 September 2014

Academic Editor: Fernando Torres

Copyright © 2014 Irwansyah et al. 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

Let and be two Galois rings. In this paper, we show how to construct normal basis in the extension of Galois rings, and we also define weakly self-dual normal basis and self-dual normal basis for over , where is considered as a free module over . Moreover, we explain a way to construct self-dual normal basis using particular system of polynomials. Finally, we show the connection between self-dual normal basis for over and the set of all invertible, circulant, and orthogonal matrices over .