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Enumeration of the bent functions of least deviation from a quadratic bent function

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Abstract

We study a construction of the bent functions of least deviation from a quadratic bent function, describe all these bent functions of 2k variables, and show that the quantity of them is 2k(21 + 1) ... (2k + 1). We find some lower bound on the number of the bent functions of least deviation from a bent function of the Maiorana-McFarland class.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    N. A. Kolomeets

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  1. N. A. Kolomeets
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Correspondence to N. A. Kolomeets.

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Original Russian Text © N.A. Kolomeets, 2012, published in Diskretnyi Analiz i Issledovanie Operatsii, 2012, Vol. 19, No. 1, pp. 41–58.

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Kolomeets, N.A. Enumeration of the bent functions of least deviation from a quadratic bent function. J. Appl. Ind. Math. 6, 306–317 (2012). https://doi.org/10.1134/S1990478912030052

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  • DOI: https://doi.org/10.1134/S1990478912030052

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