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 
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/
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     title = {On {Polynomials} of {Special} {Form} over a {Finite} {Field} of {Odd} {Characteristic} {Attaining} the {Weil} {Bound}},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Lidl R., Niderraiter G., Konechnye polya, Mir, M., 1988 | Zbl

[2] Bassalygo L. A., Zinovev V. A., “Mnogochleny spetsialnogo vida nad konechnym polem s maksimalnym modulem trigonometricheskoi summy”, UMN, 52:2 (1997), 31–44 | MR | Zbl

[3] Malyshev A. V., O predstavlenii tselykh chisel polozhitelnymi kvadratichnymi formami, Tr. MIAN, 65, Nauka, M., 1962 | MR | Zbl

[4] Bassalygo L. A., Zinovev V. A., “O mnogochlenakh nad konechnym polem chetnoi kharakteristiki s maksimalnym znacheniem modulya trigonometricheskoi summy”, Matem. zametki, 72:2 (2002), 171–177 | MR | Zbl

[5] Lidl R., Mullen G. L., Turnwald G., Dickson Polynomials, Pitman Monographs and Surveys in Pure and Applied Mathematics, 65, John Wiley and Sons, New York, 1993 | Zbl