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On realization of quadratic boolean functions by systems of linear equations

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Abstract

We describe the shortest representation of quadratic boolean functions as disiunctions of products of linear forms.

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Literature Cited

  1. Yu. I. Zhuravlev, “Set-theoretical methods of boolean algebra,” Probl. Kiber., No. 8, 5–44 (1962).

    Google Scholar 

  2. S. V. Yablonskii and O. B. Lupanov (eds.), Discrete Mathematics and Mathematical Topics in Cybernetics [in Russian], Vol. I, Nauka, Moscow (1974).

    Google Scholar 

  3. G. N. Povarov, “Mathematical theory of the design of contact (1, k)-poles,” Dokl. Akad. Nauk SSSR,100, No. 5, 909–912 (1955).

    Google Scholar 

  4. I. É. Strazdin', “Affine classification of boolean functions of five variables,” Avtomat. Vychisl. Tekh., No. 1, 1–9 (1975).

    Google Scholar 

  5. M. A. Harrison, “On the classification of Boolean functions by the general linear and affine groups,” J. SIAM,12, No. 2, 110–112 (1964).

    Google Scholar 

  6. L. E. Dickson, Linear Groups with an Exposition of the Galois Field Theory, Leipzig (1901).

  7. A. A. Albert, “Symmetric and alternating matrices in an arbitrary field,” Trans. AMS,43, 386–436 (1938).

    Google Scholar 

  8. T. Kasami and N. Tokura, “On the weight structure of Reed-Muller codes,” IEEE Trans. Inf. Theory,16, 752–759 (1970).

    Google Scholar 

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Additional information

Translated from Kibernetika, No. 1, pp. 9–14, 18, January–February, 1989.

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Aleksanyan, A.F. On realization of quadratic boolean functions by systems of linear equations. Cybern Syst Anal 25, 9–17 (1989). https://doi.org/10.1007/BF01074878

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  • DOI: https://doi.org/10.1007/BF01074878

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