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A NOTE ON SOME CHARACTER SUMS OVER FINITE FIELDS

Part of: Finite fields and commutative rings (number-theoretic aspects)

Published online by Cambridge University Press:  30 April 2015

XIWANG CAO  and
GUANGKUI XU
XIWANG CAO*
Affiliation:
Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, PR China email xwcao@nuaa.edu.cn
GUANGKUI XU
Affiliation:
Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, PR China Department of Mathematics, Huainan Normal University, Huainan 232038, PR China email xuguangkuiy@163.com
*
✉xwcao@nuaa.edu.cn
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Abstract

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In this paper, we present a decomposition of the elements of a finite field and illustrate the efficiency of this decomposition in evaluating some specific exponential sums over finite fields. The results can be employed in determining the Walsh spectrum of some Boolean functions.

Keywords

finite fieldexponential sumBoolean functionWalsh spectrum

MSC classification

Primary: 11T23: Exponential sums
Secondary: 11T71: Algebraic coding theory; cryptography
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 92 , Issue 1 , August 2015 , pp. 32 - 43
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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