Self-Dual Normal Basis of a Galois Ring

Self-Dual Normal Basis of a Galois Ring

Let R′=GR(ps,psml) and R=GR(ps,psm) 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 R′ over R, where R′ is considered as a free module over R. Moreover, we expl...

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Main Authors: Irwansyah, Intan Muchtadi-Alamsyah, Aleams Barra, Ahmad Muchlis
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2014/258187
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spelling doaj-a6f3dd965b2f405d97fc67b29180a5c02020-11-25T01:05:12ZengHindawi LimitedJournal of Mathematics2314-46292314-47852014-01-01201410.1155/2014/258187258187Self-Dual Normal Basis of a Galois RingIrwansyah0Intan Muchtadi-Alamsyah1Aleams Barra2Ahmad Muchlis3Algebra Research Group, Institut Teknologi Bandung, Bandung 40132, IndonesiaAlgebra Research Group, Institut Teknologi Bandung, Bandung 40132, IndonesiaAlgebra Research Group, Institut Teknologi Bandung, Bandung 40132, IndonesiaAlgebra Research Group, Institut Teknologi Bandung, Bandung 40132, IndonesiaLet R′=GR(ps,psml) and R=GR(ps,psm) 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 R′ over R, where R′ is considered as a free module over R. 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 R′ over R and the set of all invertible, circulant, and orthogonal matrices over R.http://dx.doi.org/10.1155/2014/258187
collection DOAJ
language English
format Article
sources DOAJ
author Irwansyah
Intan Muchtadi-Alamsyah
Aleams Barra
Ahmad Muchlis
spellingShingle Irwansyah
Intan Muchtadi-Alamsyah
Aleams Barra
Ahmad Muchlis
Self-Dual Normal Basis of a Galois Ring
Journal of Mathematics
author_facet Irwansyah
Intan Muchtadi-Alamsyah
Aleams Barra
Ahmad Muchlis
author_sort Irwansyah
title Self-Dual Normal Basis of a Galois Ring
title_short Self-Dual Normal Basis of a Galois Ring
title_full Self-Dual Normal Basis of a Galois Ring
title_fullStr Self-Dual Normal Basis of a Galois Ring
title_full_unstemmed Self-Dual Normal Basis of a Galois Ring
title_sort self-dual normal basis of a galois ring
publisher Hindawi Limited
series Journal of Mathematics
issn 2314-4629
2314-4785
publishDate 2014-01-01
description Let R′=GR(ps,psml) and R=GR(ps,psm) 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 R′ over R, where R′ is considered as a free module over R. 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 R′ over R and the set of all invertible, circulant, and orthogonal matrices over R.
url http://dx.doi.org/10.1155/2014/258187
work_keys_str_mv AT irwansyah selfdualnormalbasisofagaloisring
AT intanmuchtadialamsyah selfdualnormalbasisofagaloisring
AT aleamsbarra selfdualnormalbasisofagaloisring
AT ahmadmuchlis selfdualnormalbasisofagaloisring
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