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Divisibility properties of classical binary Kloosterman sums |
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| Authors: | Pascale Charpin Victor Zinoviev |
| Institution: | a INRIA, Domaine de Voluceau-Rocquencourt, BP 105 - 78153, Le Chesnay, France b The Selmer Center, Department of Informatics, University of Bergen, PB 7803, N-5020, Bergen, Norway c Institute for Problems of Information Transmission of the Russian Academy of Sciences, Bol’shoi Karetnyi per. 19, GSP-4, Moscow, 101447, Russia |
| Abstract: | Let K(a) be the so-called classical Kloosterman sum over  . In this paper, we compute K(a) modulo 24 for even m, completing our previous results for odd m. We extensively study the links between K(a) and other exponential sums, especially the cubic sums. We point out (as we did for odd m) that the values K(a) are involved in the computation of the weight distributions of cosets of primitive narrow sense extended BCH codes of length 2m and minimum distance 8. We also complete some recent results on K(a)−1 modulo 3. |
| Keywords: | Binary primitive narrow sense BCH code Coset Coset weight distribution Exponential sum Cubic sum Classical Kloosterman sum Inverse cubic sum Partial sum |
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