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Paper 2009/563
A Family of $p$-ary Binomial Bent Functions
Dabin Zheng and Xiangyong Zeng and Lei Hu
Abstract
For a prime $p$ with $p\equiv 3\,({\rm mod}\, 4)$ and an odd number $m$, the Bentness of the $p$-ary binomial function $f_{a,b}(x)={\rm Tr}_{1}^n(ax^{p^m-1})+{\rm Tr}_{1}^2(bx^{\frac{p^n-1}{4}})$ is characterized, where $n=2m$, $a\in \bF_{p^n}^*$, and $b\in \bF_{p^2}^*$. The necessary and sufficient conditions of $f_{a,b}(x)$ being Bent are established respectively by an exponential sum and two sequences related to $a$ and $b$. For the special case of $p=3$, we further characterize the Bentness of the ternary function $f_{a,b}(x)$ by the Hamming weight of a sequence.
Metadata
- Available format(s)
- Category
- Foundations
- Publication info
- Published elsewhere. Unknown where it was published
- Contact author(s)
- dbzheng @ gucas ac cn
- History
- 2009-11-23: received
- Short URL
- https://ia.cr/2009/563
- License
-
CC BY