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Boolean functions with two distinct Walsh coefficients

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Abstract

Are there other Boolean functions having two distinct Walsh coefficients except affine Boolean functions and maximal nonlinear (i.e. bent) Boolean functions? This paper proves that all Boolean functions with exactly two distinct Walsh coefficients are just the two known classes of affine and bent Boolean functions and the Boolean functions obtained by modifying the value of affine or bent Boolean functions at x = 0.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Henan University of Science and Technology, 471003, Luoyang, China

    Ziran Tu

  2. State Key Laboratory of Information Security, Graduate University of Chinese Academy of Sciences, 100049, Beijing, China

    Dabin Zheng & Lei Hu

  3. Faculty of Mathematics and Computer Science, Hubei University, 430062, Wuhan, China

    Dabin Zheng & Xiangyong Zeng

Authors
  1. Ziran Tu
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  2. Dabin Zheng
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  3. Xiangyong Zeng
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  4. Lei Hu
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Corresponding author

Correspondence to Dabin Zheng.

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Tu, Z., Zheng, D., Zeng, X. et al. Boolean functions with two distinct Walsh coefficients. AAECC 22, 359–366 (2011). https://doi.org/10.1007/s00200-011-0155-3

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  • DOI: https://doi.org/10.1007/s00200-011-0155-3

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