1. Planarity of mappings on finite fields.
- Author
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Yang, Minghui, Zhu, Shixin, and Feng, Keqin
- Subjects
- *
MATHEMATICAL mappings , *FINITE fields , *NONLINEAR theories , *PERMUTATIONS , *MATHEMATICAL proofs , *MATHEMATICAL analysis - Abstract
Let q be a power of an odd prime, and be the trace mapping. A mapping is called planar (or perfect nonlinear) on if for any non-zero , the difference mapping is a permutation where for , . Kyureghyan and Özbudak (2012) [8] considered the planarity of mappings on for and proved that there is no planar for . For the case and , they raised three conjectures. In this paper we prove the third conjecture which says that there is no planar for , by using Kloosterman sums. Our proof also works for case , so we present a new proof of the Kyureghyan–Özbudak result. For case , we present an elementary proof of the first conjecture which says that there is no planar for . [ABSTRACT FROM AUTHOR]
- Published
- 2013
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