Self-Dual Normal Basis of a Galois Ring

Abstract EN

Let R ′ = G R ( p s , p s m l ) and R = G R ( p s , p s m ) 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 .