On Polynomials of Special Form over a Finite Field of Odd Characteristic Attaining the Weil Bound

摘要

An explicit construction of polynomials over a finite field of odd characteristic, for which the absolute value of trigonometric sums attains the Weil bound, is based on the construction of cyclic matrices of given rank. Dickson polynomials of the second kind play an essential role in the study of such matrices.