On Integer Values of Kloosterman Sums
| Autor: | Keijo Väänänen, Keijo Kononen, Marko J. Rinta-aho |
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| Rok vydání: | 2010 |
| Předmět: | |
| Zdroj: | IEEE Transactions on Information Theory. 56:4011-4013 |
| ISSN: | 1557-9654 0018-9448 |
| DOI: | 10.1109/tit.2010.2050806 |
| Popis: | This paper considers rational integer values of Kloosterman sums over finite fields of characteristic p > 3. We shall prove two main results. The first one is a congruence relation satisfied by possible integer values. One consequence is that there are no Kloosterman zeroes in the case of characteristic p > 3, which generalizes recent works by Shparlinski, Moisio, and Lisonek on this subject. This, in turn, implies that there are no Dillon type bent functions in the case p > 3 , thus answering a question posed recently by Helleseth and Kholosha. Our other main result states that the Kloosterman sum obtains an integer value at a point if and only if the same sum lifted to any extension field remains an integer. |
| Databáze: | OpenAIRE |
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