In this paper ideals of certain group algebra are used to prove results on k -normal elements over finite fields, including ways to determine them from normal elements by means of polynomials and circulant matrices. Alternative proofs of results appearing in [4] are also provided. [ABSTRACT FROM AUTHOR]
Let F q denote the finite field of order q . In this paper, some new classes of permutation polynomials of the form ( x p m − x + δ ) s + x over F p 2 m are obtained by determining the number of solutions of certain equations. [ABSTRACT FROM AUTHOR]
In this paper, we propose a class of permutation polynomials over the finite field F 2 2 m for odd m . These permutations are generally quadrinomials, and some permutation trinomials can also be obtained. [ABSTRACT FROM AUTHOR]