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Generalized Rotation Symmetric and Dihedral Symmetric Boolean Functions − 9 Variable Boolean Functions with Nonlinearity 242

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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4851))

Abstract

Recently, 9-variable Boolean functions having nonlinearity 241, which is strictly greater than the bent concatenation bound of 240, have been discovered in the class of Rotation Symmetric Boolean Functions (RSBFs) by Kavut, Maitra and Yücel. In this paper, we present several 9-variable Boolean functions having nonlinearity of 242, which we obtain by suitably generalizing the classes of RSBFs and Dihedral Symmetric Boolean Functions (DSBFs). These functions do not have any zero in the Walsh spectrum values, hence they cannot be made balanced easily. This result also shows that the covering radius of the first order Reed-Muller code R(1, 9) is at least 242.

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Authors and Affiliations

  1. Department of Electrical Engineering and Institute of Applied Mathematics, Middle East Technical University (METU − ODTÜ), 06531, Ankara, Türkiye,  

    Selçuk Kavut & Melek Diker Yücel

Authors
  1. Selçuk Kavut
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  2. Melek Diker Yücel
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Serdar Boztaş Hsiao-Feng (Francis) Lu

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Kavut, S., Yücel, M.D. (2007). Generalized Rotation Symmetric and Dihedral Symmetric Boolean Functions − 9 Variable Boolean Functions with Nonlinearity 242. In: Boztaş, S., Lu, HF.(. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2007. Lecture Notes in Computer Science, vol 4851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77224-8_37

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  • DOI: https://doi.org/10.1007/978-3-540-77224-8_37

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77223-1

  • Online ISBN: 978-3-540-77224-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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