Geodesic
On Polynomials of Special Form over a Finite Field of Odd Characteristic Attaining the Weil Bound
Matematičeskie zametki, Tome 78 (2005) no. 1, pp. 16-25

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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. 
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     author = {L. A. Bassalygo and V. A. Zinov'ev},
     title = {On {Polynomials} of {Special} {Form} over a {Finite} {Field} of {Odd} {Characteristic} {Attaining} the {Weil} {Bound}},
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L. A. Bassalygo; V. A. Zinov'ev. On Polynomials of Special Form over a Finite Field of Odd Characteristic Attaining the Weil Bound. Matematičeskie zametki, Tome 78 (2005) no. 1, pp. 16-25. http://geodesic.mathdoc.fr/item/MZM_2005_78_1_a1/