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

This article is cited in 2 scientific papers (total in 2 papers)

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

Full text: PDF file (186 kB)
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English version:
Mathematical Notes, 2002, 72:2, 152–157

Bibliographic databases:

UDC: 512.6
Received: 27.11.2001

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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\pages 171--177
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    Citing articles on Google Scholar: Russian citations, English citations
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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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    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  mathnet  crossref  crossref  mathscinet  isi  elib  elib
  • Математические заметки Mathematical Notes
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