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The connection between quadratic bent–negabent functions and the Kerdock code

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Abstract

In this paper we prove that all bent functions in the Kerdock code, except for the coset of the symmetric quadratic bent function, are bent–negabent. In this direction, we characterize the set of quadratic bent–negabent functions and show some results connecting quadratic bent–negabent functions and the Kerdock code. Further, we note that there are bent–negabent preserving nonsingular transformations outside the well known class of orthogonal ones that might provide additional functions in the bent–negabent set. This is the first time we could identify non-orthogonal (nonsingular) linear transformations that preserve bent–negabent property for a special subset.

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Acknowledgements

The authors would like to thank the reviewers for extraordinarily useful criticisms and suggestions, and for providing us with a better code of Fig. 1. The paper was partly written while the first author visited the second and third authors at the Indian Statistical Institute, Kolkata. He would like to thank the hosts and the institute for hospitality and excellent working conditions.

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Authors and Affiliations

  1. Department of Applied Mathematics, Naval Postgraduate School, Monterey, USA

    Pantelimon Stănică

  2. R. C. Bose Centre for Security and Cryptology, Indian Statistical Institute, Kolkata, India

    Bimal Mandal

  3. Applied Statistics Unit, Indian Statistical Institute, Kolkata, India

    Subhamoy Maitra

Authors
  1. Pantelimon Stănică
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  2. Bimal Mandal
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  3. Subhamoy Maitra
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Correspondence to Pantelimon Stănică.

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Stănică, P., Mandal, B. & Maitra, S. The connection between quadratic bent–negabent functions and the Kerdock code. AAECC 30, 387–401 (2019). https://doi.org/10.1007/s00200-019-00380-4

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  • DOI: https://doi.org/10.1007/s00200-019-00380-4

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