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...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2014-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/258187 |
| Summary: | 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. |
|---|---|
| ISSN: | 2314-4629 2314-4785 |