## 留言板

 引用本文: 赵海霞, 李文宇, 韦永壮. 基于迹函数的negabent函数构造[J]. 电子与信息学报, 2024, 46(1): 335-343.
ZHAO Haixia, LI Wenyu, WEI Yongzhuang. Construction of Negabent Function Based on Trace Function over Finite Field[J]. Journal of Electronics & Information Technology, 2024, 46(1): 335-343. doi: 10.11999/JEIT230001
 Citation: ZHAO Haixia, LI Wenyu, WEI Yongzhuang. Construction of Negabent Function Based on Trace Function over Finite Field[J]. Journal of Electronics & Information Technology, 2024, 46(1): 335-343.

## 基于迹函数的negabent函数构造

##### doi: 10.11999/JEIT230001

###### 通讯作者: 韦永壮　walker_wyz@guet.edu.cn
• 中图分类号: TN918.2

## Construction of Negabent Function Based on Trace Function over Finite Field

Funds: The National Natural Science Foundation of China (62162016), Guangxi Natural Science Foundation (2019GXNSFGA245004)
• 摘要: Negabent函数是一种具有最优自相关性、较高非线性度的布尔函数，在密码学、编码理论及组合设计中都有着广泛的应用。该文基于有限域上的迹函数，将其与置换多项式相结合，提出两种构造negabent函数的方法。所构造的两类negabent函数均具备${\text{Tr}}_1^k(\lambda {x^{{2^k} + 1}}) + {\text{Tr}}_1^n(ux){\text{Tr}}_1^n(vx) + {\text{Tr}}_1^n(mx){{\rm{Tr}}} _1^n(dx)$形式：构造方法1通过调整$\lambda ,{\text{ }}u,{\text{ }}v,{\text{ }}m$中的3个参数来获得negabent函数，特别地，当$\lambda$≠1时，能得到$({2^{n - 1}} - 2)({2^n} - 1)({2^n} - 4)$个negabent函数；构造方法2通过调整$\lambda ,{\text{ }}u,{\text{ }}v,{\text{ }}m,{\text{ }}d$中的4个参数来获得negabent函数，特别地，当$\lambda$≠1时，至少能够得到${2^{n - 1}}[({2^{n - 1}} - 2)({2^{n - 1}} - 3) + {2^{n - 1}} - 4]$个negabent函数。
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##### 出版历程
• 收稿日期:  2023-01-09
• 修回日期:  2023-06-09
• 网络出版日期:  2023-06-14
• 刊出日期:  2024-01-17

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