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New Kloosterman sums identities over $$\mathbb F_{2^m}$$ for all $$m$$. (English) Zbl 1081.11077
Summary: Recently, [Discrete Math. 268, No. 1-3, 337–341 (2003; Zbl 1049.11134)] D. J. Shin and W. Sung found new identities for Kloosterman sums over $$\mathbb F_{2^m}$$ with odd $$m$$. They posed the question whether similar results could be obtained for even $$m$$. In this paper, we give a positive answer to this question. We present new results that hold for any $$m$$ and include as special cases the results of Shin and Sung in the case where $$m$$ is odd.

##### MSC:
 11T24 Other character sums and Gauss sums 11L05 Gauss and Kloosterman sums; generalizations
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##### References:
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