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On classical Kloosterman sums

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Abstract

It is a survey on the Kloosterman sums. We consider the known results on the classical Kloosterman sums, i.e. the Kloosterman sums over the finite fields \(\mathbb {F}_{q}\) of order q = pm, p ≥ 2 is prime.

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Acknowledgements

The author would like to thank L. A. Bassalygo, D. V. Zinoviev and anonymous reviewers for useful remarks which permit to improve the original variant of the paper.

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  1. Harkevich Institute for Problems of Information Transmission, Russian Academy of Sciences, Bol’shoi Karetnyi per. 19, GSP-4, Moscow, 127994, Russia

    V. A. Zinoviev

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Dedicated to Tor Helleseth’s 70th birthday

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Zinoviev, V.A. On classical Kloosterman sums. Cryptogr. Commun. 11, 461–496 (2019). https://doi.org/10.1007/s12095-019-00357-7

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