Abstract
In this paper we investigate the propagation criterion for strict majority symmetric Boolean functions. With the use of the theory of Krawtchouk polynomials it is shown that vectors whose Hamming weight differs from n/2 by at most 1/2 satisfy the propagation criterion for strict majority functions in n variables, where ⌊n/2⌋ is odd.
Originally published in Diskretnaya Matematika (2023) 35, №1, 62–70 (in Russian).
Acknowledgment
In conclusion the author expresses sincere gratitude to A. V. Tarasov for valuable remarks and suggestions that contributed to the improvement of the text.
References
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Articles in the same Issue
- Frontmatter
- Generation of n-quasigroups by proper families of functions
- Boolean functions constructed using digital sequences of linear recurrences
- On the sets of the propagation criterion for strict majority Boolean functions
- Branching processes in random environment with freezing
- Limit joint distribution of the statistics of «Monobit test», «Frequency Test within a Block» and «Binary Matrix Rank Test»
- On random mappings with restrictions on sizes of components
Articles in the same Issue
- Frontmatter
- Generation of n-quasigroups by proper families of functions
- Boolean functions constructed using digital sequences of linear recurrences
- On the sets of the propagation criterion for strict majority Boolean functions
- Branching processes in random environment with freezing
- Limit joint distribution of the statistics of «Monobit test», «Frequency Test within a Block» and «Binary Matrix Rank Test»
- On random mappings with restrictions on sizes of components