Rotation-Symmetric Functions And Type K-Gaussian Normal Bases Over Finite Fields

Let Fqn be the extension of q elements finite field Fq withdegree n(n > 1). First, by using properties of polynomials over finite fields, thisthesis gives a formula for the determinant of a type of n×n symmetric circulantmatrices over F2. And so, a kind of nonsingular symmetric circulant matricesare obtained. Secondly, the dual basis B of the type k-Gaussian normal basisN of Fqn over Fq is obtained by using an elementary method. Finally, thecorrespondence between multiplication tables of N and B is given.