Skip to main content
Log in

Abstract

Symmetric Boolean polynomials are a natural and long-term object of studies in many branches of discrete mathematics. New facts concerning symmetric Boolean polynomials are presented, and applications in cryptography and for determining the number of zeros of symmetric polynomials are proposed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. A. A. Aleksanyan, Disjunctive Normal Forms over Linear Functions (Erevanskii Gos. Univ., Yerevan, 1990) [in Russian].

    MATH  Google Scholar 

  2. E. Eherenfeucht and M. Karpinski, “The Computational Complexity of (XOR, AND)-Counting Problems,” Preprint (Univ. of Bohn, Bohn, 1989).

    Google Scholar 

  3. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes (North-Holland, Amsterdam, 1977; Radio i Svyaz’, Moscow, 1979).

    MATH  Google Scholar 

  4. V. K. Leont’ev and O. O. Moreno, “On the Zeros of Boolean Polynomials,” Zh. Vychisl. Mat. Mat. Fiz. 38, 1608–1615 (1998) [Comput. Math. Math. Phys. 38, 1542–1549 (1998)].

    MathSciNet  Google Scholar 

  5. V. Leontiev and O. Moreno, “On the Boolean Polynomials:” Preprint (Univ. of Puerto-Rico, Puerto-Rico, 1995).

    Google Scholar 

  6. V. K. Leont’ev, “Certain Problems Associated with Boolean Polynomials,” Zh. Vychisl. Mat. Mat. Fiz. 39, 1045–1054 (1999) [Comput. Math. Math. Phys. 39, 1006–1015 (1999)].

    MathSciNet  Google Scholar 

  7. V. N. Sachkov, Combinatorial Methods in Discrete Mathematics (Nauka, Moscow, 1977) [in Russian].

    Google Scholar 

  8. I. G. Macdonald, Symmetric Functions and Hall Polynomials (Clarendon, Oxford, 1979; Mir, Moscow, 1985).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. K. Leont’ev.

Additional information

Original Russian Text © V.K. Leont’ev, 2010, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2010, Vol. 50, No. 8, pp. 1520–1531.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Leont’ev, V.K. Symmetric boolean polynomials. Comput. Math. and Math. Phys. 50, 1447–1458 (2010). https://doi.org/10.1134/S0965542510080142

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0965542510080142

Key words

Navigation