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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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