Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Further results on constructions of generalized bent Boolean functions

广义 bent 函数构造的进一步研究



对文献 [Stanica P, Martinsen T, Gangopadhyay S, Singh B J. Bent and generalized bent Boolean functions. Des. Codes Cryptogr., 2013, 69: 77–94.]中的三个重要结果做了进一步的研究。 第一, 通过对关于 2 个变元对称的 n+2 元广义 bent 函数的研究, 刻画了一类关于 m 个变元对称的 n+m 元广义 bent 函数, 其中 m 为偶数。 第二, 基于广义 bent 函数已知抽象结果, 给出了构造该类广义 bent 函数几种具体的新方法, 提高了过去的结果。

This is a preview of subscription content, log in to check access.


  1. 1

    Rothaus O S. On ‘bent’ functions. J Combin Theory A, 1976, 20: 300–305

  2. 2

    Carlet C. Two new classes of bent functions. In: Proceedings of Workshop on the Theory and Application of Cryptographic Techniques, Lofthus, 1994. 77–101

  3. 3

    Zhang F, Wei Y, Pasalic E. Constructions of bentnegabent functions and their relation to the completedMaiorana-McFarland class. IEEE Trans Inf Theory, 2015, 61: 1496–1506

  4. 4

    Zhang W G, Xiao G Z. Constructions of almost optimal resilient Boolean functions on large even number of variables. IEEE Trans Inf Theory, 2009, 55: 5822–5831

  5. 5

    Zhang W G, Jiang F Q, Tang D. Construction of highly nonlinear resilient Boolean functions satisfying strict avalanche criterion. Sci China Inf Sci, 2014, 57: 049101

  6. 6

    Schmidt K U. Quaternary constant-amplitude codes for multicode CDMA. IEEE Trans Inf Theory, 2009, 55: 1824–1832

  7. 7

    Solé P, Tokareva N. Connections between quaternary and binary bent functions. /2009/544.pdf

  8. 8

    Stănică P, Gangopadhyay S, Chaturvedi A, et al. Nega-Hadamard transform, bent and negabent functions. In: Proceedings of 6th International Conference on Sequences and Their Applications, Paris, 2010. 359–372

  9. 9

    Stănică P, Martinsen T, Gangopadhyay S, et al. Bent and generalized bent Boolean functions. Des Codes Cryptogr, 2013, 69: 77–94

  10. 10

    Zhao Y, Li H L. On bent functions with some symmetric properties. Discret Appl Math, 2006, 154: 2537–2543

Download references

Author information

Correspondence to Shixiong Xia.

Electronic supplementary material

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zhang, F., Xia, S., Stănică, P. et al. Further results on constructions of generalized bent Boolean functions. Sci. China Inf. Sci. 59, 059102 (2016).

Download citation


  • 布尔函数
  • 广义布尔函数
  • bent 函数
  • 广义 bent 函数