Abstract
We study trigonometric sums in finite fields \(F_Q \). The Weil estimate of such sums is well known: \(|S(f)| \leqslant ({\text{deg }}f - 1)\sqrt Q \), where f is a polynomial with coefficients from F(Q). We construct two classes of polynomials f, \((Q,2) = 2\), for which \(|S(f)|\) attains the largest possible value and, in particular, \(|S(f)| = ({\text{deg }}f - 1)\sqrt Q \).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
L. A. Bassalygo and V. A. Zinov'ev, “Polynomials of a special form over a finite field with maximum absolute value of the trigonometric sum,” Uspekhi Mat. Nauk [Russian Math. Surveys], 52 (1997), no. 2, 31–44.
R. Lidl and H. Niederreiter, Finite Fields, Addison-Wesley, Reading, MA, 1983.
O. Moreno and C. J. Moreno, “The MacWilliams-Sloane conjecture on the tightness of the Carlitz-Uchiyama bound and the weights of duals of BCH codes,” IEEE Trans. Information Theory, 40 (1994), no. 6, 1894–1907.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bassalygo, L.A., Zinov'ev, V.A. On Polynomials over a Finite Field of Even Characteristic with Maximum Absolute Value of the Trigonometric Sum. Mathematical Notes 72, 152–157 (2002). https://doi.org/10.1023/A:1019837625836
Issue Date:
DOI: https://doi.org/10.1023/A:1019837625836