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 Mat. Zametki, 2002, Volume 72, Issue 2, Pages 171–177 (Mi mz412)

On Polynomials over a Finite Field of Even Characteristic with Maximum Absolute Value of the Trigonometric Sum

L. A. Bassalygo, V. A. Zinov'ev

Institute for Information Transmission Problems, Russian Academy of Sciences

Abstract: We study trigonometric sums in finite fields $F_Q$. The Weil estimate of such sums is well known: $|S(f)|\le (\deg f-1)\sqrt Q$, 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, $|S(f)|=(\deg f-1)\sqrt Q$.

DOI: https://doi.org/10.4213/mzm412

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English version:
Mathematical Notes, 2002, 72:2, 152–157

Bibliographic databases:

UDC: 512.6

Citation: L. A. Bassalygo, V. A. Zinov'ev, “On Polynomials over a Finite Field of Even Characteristic with Maximum Absolute Value of the Trigonometric Sum”, Mat. Zametki, 72:2 (2002), 171–177; Math. Notes, 72:2 (2002), 152–157

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/mz412
• https://doi.org/10.4213/mzm412
• http://mi.mathnet.ru/eng/mz/v72/i2/p171

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This publication is cited in the following articles:
1. L. A. Bassalygo, V. A. Zinov'ev, “On Polynomials of Special Form over a Finite Field of Odd Characteristic Attaining the Weil Bound”, Math. Notes, 78:1 (2005), 14–22
2. L. A. Bassalygo, V. A. Zinov'ev, “Polynomials of Special Form over a Finite Field with an Exact Value of the Trigonometric Sum”, Math. Notes, 82:1 (2007), 3–9
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