New Secondary Constructions of Generalized Bent Functions
New Secondary Constructions of Generalized Bent Functions
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DOI：
10.1049/cje.2021.08.003
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发表时间：
2021-11
影响因子：
1.2
通讯作者：
Yan Zhiyao;Ke Pinhui;C. Zhixiong
中科院分区：
文献类型：
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作者：
Yan Zhiyao;Ke Pinhui;C. Zhixiong
给出了广义Bent函数的三种新的二次构造。利用Carlet等人提出的间接和方法，我们给出了广义Bent函数的二次构造。还研究了由四个初始函数构造广义Bent函数的新方法。我们证明了通过选择适当的初始函数和参数，许多已知的结构可以作为特例从我们提出的结构中得到。通过修改新的构造，由两个初始广义Bent函数得到了一种新的广义Bent函数的二次构造。对于二元情形，用我们的方法给出了Bent函数的对偶函数，它们与间接和具有相同的公式。
Three new secondary constructions of generalized bent functions are presented. We provide a secondary construction of generalized bent functions from indirect sum methods proposed by Carlet et al. A new secondary construction of generalized bent functions from four initial functions is also investigated. We demonstrate that many known constructions can be derived from our proposed construction as special cases by choosing proper initial functions and parameters. By modifying the new construction, a novel secondary construction of generalized bent functions from two initial generalized bent functions is obtained. For the binary case, the dual functions of the bent functions by our method are presented, which share the same formula as the indirect sum.