New secondary constructions of Bent functions

  • Fengrong Zhang
  • Claude Carlet
  • Yupu Hu
  • Wenzheng Zhang
Original Paper


In this paper, we first present a novel secondary construction of bent functions (building new bent functions from two already defined ones). Furthermore, the algebraic degree and algebraic immunity of the constructed functions are analysed. Finally, we apply the construction using as initial functions some specific bent functions and then specify sufficient conditions for the resulting bent functions not to be contained in the completed Maiorana–McFarland class. In the second part of the paper, we present a corrigendum of “Constructions of bent–negabent functions and their relation to the completed Maiorana–McFarland Class” (IEEE Trans Inf Theory 61(3):1496–1506, 2015).


Boolean function Bent function High nonlinearity  Algebraic degree 

Mathematics Subject Classification

06E30 94A60 



The work of F. Zheng was supported in part by National Science Foundation of China (61303263), and in part by the Fundamental Research Funds for the Central Universities (2013QNA26), in part by the China Postdoctoral Science Foundation funded project (2014M562494, 2015T80600), and in part by the Jiangsu Planned Projects for Postdoctoral Research Funds (1401056B). The first author is grateful to Prof. Enes Pasalic and Yongzhuang Wei for valuable discussions and suggestions.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Fengrong Zhang
    • 1
    • 2
  • Claude Carlet
    • 3
  • Yupu Hu
    • 2
  • Wenzheng Zhang
    • 4
  1. 1.School of Computer Science and TechnologyChina University of Mining and TechnologyXuzhouPeople’s Republic of China
  2. 2.Xidian UniversityState Key Laboratory of Integrated Services NetworksXi’anPeople’s Republic of China
  3. 3.Department of Mathematics, LAGA, CNRS, (UMR 7539), Universities of Paris 8 and Paris 13Sorbonne Paris CitéSaint-Denis CedexFrance
  4. 4.Science and Technology on Communication Security Laboratory, The 30th Research Institute of China Electronics Technology Group CorporationChengduPeople’s Republic of China

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