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Diskr. Mat., 2017, Volume 29, Issue 1, Pages 114–125 (Mi dm1409)  

This article is cited in 1 scientific paper (total in 1 paper)

Estimating the level of affinity of a quadratic form

A. V. Cheremushkin

Research Institute "Kvant"

Abstract: The level of affinity of a Boolean function is defined as the minimum number of variables such that assigning any particular values to these variables makes the function affine. The generalized level of affinity is defined as the minimum number of linear combinations of variables the values of which may be specified in such a way that the function becomes affine. For a quadratic form of rank $2r$ the generalized level of affinity is equal to $r$. We present some properties of the distribution of the rank of the random quadratic form and, as a corollary, derive an asymptotic estimate for the generalized level of affinity of quadratic forms.

Keywords: Boolean functions, quadratic forms, level of affinity.

DOI: https://doi.org/10.4213/dm1409

Full text: PDF file (433 kB)
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English version:
Discrete Mathematics and Applications, 2017, 27:6, 339–347

Bibliographic databases:

UDC: 519.115+519.719.1
Received: 19.05.2016

Citation: A. V. Cheremushkin, “Estimating the level of affinity of a quadratic form”, Diskr. Mat., 29:1 (2017), 114–125; Discrete Math. Appl., 27:6 (2017), 339–347

Citation in format AMSBIB
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\paper Estimating the level of affinity of a quadratic form
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\pages 114--125
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\jour Discrete Math. Appl.
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\pages 339--347
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. G. Ryabov, “O stepeni ogranichenii funktsii $q$-znachnoi logiki na lineinye mnogoobraziya”, PDM, 2019, no. 45, 13–25  mathnet  crossref
  • Дискретная математика
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