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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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/258187 |
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| author | Irwansyah Intan Muchtadi-Alamsyah Aleams Barra Ahmad Muchlis |
| author_facet | Irwansyah Intan Muchtadi-Alamsyah Aleams Barra Ahmad Muchlis |
| author_sort | Irwansyah |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-a6f3dd965b2f405d97fc67b29180a5c0 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-a6f3dd965b2f405d97fc67b29180a5c02025-02-03T05:51:04ZengWileyJournal 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 |
| spellingShingle | Irwansyah Intan Muchtadi-Alamsyah Aleams Barra Ahmad Muchlis Self-Dual Normal Basis of a Galois Ring Journal of Mathematics |
| title | 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_short | Self-Dual Normal Basis of a Galois Ring |
| title_sort | self dual normal basis of a galois ring |
| 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 |