Estimating the level of affinity of a quadratic form
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Aleksandr V. Cheremushkin
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.
Originally published in Diskretnaya Matematika (2017) 29, №1, 114–125 (in Russian).
References
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© 2017 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Estimating the level of affinity of a quadratic form
- Cyclic decomposition of sets, set-splitting digraphs and cyclic classes of risk-free games
- Large deviations of branching processes with immigration in random environment
- On the probability of existence of substrings with the same structure in a random sequence
- Linearly realizable automata
- On the number of labeled outerplanar k-cycle blocks
- Convergence of the sequence of the Pearson statistics values to the normalized square of the Bessel process
Articles in the same Issue
- Frontmatter
- Estimating the level of affinity of a quadratic form
- Cyclic decomposition of sets, set-splitting digraphs and cyclic classes of risk-free games
- Large deviations of branching processes with immigration in random environment
- On the probability of existence of substrings with the same structure in a random sequence
- Linearly realizable automata
- On the number of labeled outerplanar k-cycle blocks
- Convergence of the sequence of the Pearson statistics values to the normalized square of the Bessel process
