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International Symposium on Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes

AAECC 1993: Applied Algebra, Algebraic Algorithms and Error-Correcting Codes pp 231–243Cite as

Exponential sums as discrete fourier transform with invariant phase functions

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 673))

Abstract

We give estimates for exponential sums over finite fields in several variables. We study the case where the phase is either quadratic or more generally invariant under the action of a finite group. The bounds obtained are better than the general ones; they imply some estimates for certain sums in one variable, and for the number of solutions of the trace equation Tr(x d + vx)=0. In an appendix we discuss the link between exponential sums and bent functions.

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Authors and Affiliations

  1. Laboratoire de Mathématiques Discrètes du C.N.R.S., Luminy Case 930, 13288, Marseille cedex 9, France

    Gilles Lachaud

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  1. Gilles Lachaud
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Gérard Cohen Teo Mora Oscar Moreno

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© 1993 Springer-Verlag Berlin Heidelberg

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Lachaud, G. (1993). Exponential sums as discrete fourier transform with invariant phase functions. In: Cohen, G., Mora, T., Moreno, O. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1993. Lecture Notes in Computer Science, vol 673. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56686-4_46

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  • DOI: https://doi.org/10.1007/3-540-56686-4_46

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56686-1

  • Online ISBN: 978-3-540-47630-6

  • eBook Packages: Springer Book Archive

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