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Abstract
We give explicit evaluations of Walsh transforms of Gold type functions\(f(x)=\mathrm{Tr}_K\left( x^{2^a+1}+x^{2^b+1} \right) \),\(0 \le a < b\) when\(\gcd \left( b-a, k \right) =\gcd \left( b+a, k \right) \) and Kasami-Welch type functions\(f(x)=\mathrm{Tr}_K\left( x^{\frac{2^{ta}+1}{2^a+1}} \right) \), whent is odd,\(\gcd \left( 2^k -1, 2^a + 1\right) =1\),k is even. Therefore we correct a recent result of Roy’2012, we solve an open problem stated in Roy’2012 and we improve and generalize some results of Roy’2012 and Lahtonen-McGuire-Ward’2007.
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Acknowledgements
We would like to thank the anonymous reviewers for their insightful and helpful comments that improved the presentation of this paper.
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Department of Mathematics, Middle East Technical University, Dumlupınar Bul., No:1, 06800, Ankara, Turkey
Ayhan Coşgun
Department of Mathematics and Institute of Applied Mathematics, Middle East Technical University, Dumlupınar Bul., No:1, 06800, Ankara, Turkey
Ferruh Özbudak
Department of Mathematical Sciences, Aalborg University, Aalborg, Denmark
Ferruh Özbudak
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Correspondence toAyhan Coşgun.
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University of Rennes, Rennes, France
Sylvain Duquesne
University of Leuven, Leuven, Belgium
Svetla Petkova-Nikova
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Coşgun, A., Özbudak, F. (2016). A Correction and Improvements of Some Recent Results on Walsh Transforms of Gold Type and Kasami-Welch Type Functions. In: Duquesne, S., Petkova-Nikova, S. (eds) Arithmetic of Finite Fields. WAIFI 2016. Lecture Notes in Computer Science(), vol 10064. Springer, Cham. https://doi.org/10.1007/978-3-319-55227-9_17
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