کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4582896 | 1630380 | 2013 | 7 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Planarity of mappings x(Tr(x)âα2x) on finite fields
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
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چکیده انگلیسی
Let q be a power of an odd prime, n⩾3 and Trn:FqnâFq be the trace mapping. A mapping f=f(x):FqnâFqn is called planar (or perfect nonlinear) on Fqn if for any non-zero aâFqn, the difference mapping Df,a:FqnâFqn is a permutation where for xâFqn, Df,a(x)=f(x+a)âf(x). Kyureghyan and Ãzbudak (2012) [8] considered the planarity of mappings fn,α(x)=x(Trn(x)âα2x) on Fqn for αâFqn and proved that there is no planar fn,α for n⩾5. For the case n=3 and n=4, they raised three conjectures. In this paper we prove the third conjecture which says that there is no planar fn,α for n=4, by using Kloosterman sums. Our proof also works for case n⩾5, so we present a new proof of the Kyureghyan-Ãzbudak result. For case n=3, we present an elementary proof of the first conjecture which says that there is no planar f3,α for αâFq\{2,4}.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Finite Fields and Their Applications - Volume 23, September 2013, Pages 1-7
Journal: Finite Fields and Their Applications - Volume 23, September 2013, Pages 1-7
نویسندگان
Minghui Yang, Shixin Zhu, Keqin Feng,