Lower bound on the size of the largest metrically regular subset of the boolean cube | Applied Discrete Mathematics. Supplement. 2018. № 11. DOI: 10.17223/2226308X/11/4

HomeIssuesLower bound on the size of the largest metrically regular subset of the boolean cube | Applied Discrete Mathematics. Supplement. 2018. № 11. DOI: 10.17223/2226308X/11/4

Lower bound on the size of the largest metrically regular subset of the boolean cube

Strongly metrically regular subsets of the Boolean cube are studied. Iterative constructions of strongly metrically regular sets are presented. Formula for calculating the number of sets obtainable using these constructions is given. Special families of strongly regular sets are constructed and sizes of sets from these families are calculated. Obtained values give us lower bound on the size of the largest metrically regular subset of the Boolean cube with fixed covering radius.

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Keywords

metric complement, metrically regular set, метрическое дополнение, метрически регулярное множество

Authors

NameOrganizationE-mail
Oblaukhov A. K.Novosibirsk State Universityoblaukhov@gmail.com
Всего: 1

References

Cusick T. W. and Stanica P. Cryptographic Boolean Functions and Applications. Academic Press, 2017. 288 p.
Tokareva N. Duality between bent functions and affine functions // Discr. Math. 2012. V. 312. No. 3. P. 666-670.
Облаухов А. К. О метрическом дополнении подпространств булева куба // Дискретный анализ и исследование операций. 2016. Т. 23. №3. С. 93-106.
Lower bound on the size of the largest metrically regular subset of the boolean cube | Applied Discrete Mathematics. Supplement. 2018. № 11. DOI: 10.17223/2226308X/11/4

Lower bound on the size of the largest metrically regular subset of the boolean cube | Applied Discrete Mathematics. Supplement. 2018. № 11. DOI: 10.17223/2226308X/11/4