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Sib. Èlektron. Mat. Izv., 2007, Volume 4, Pages 292–295 (Mi semr158)  

This article is cited in 17 scientific papers (total in 17 papers)

Research papers

Perfect colorings of the $12$-cube that attain the bound on correlation immunity

D. G. Fon-Der-Flaass

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We construct perfect $2$-colorings of the $12$-hypercube that attain our recent bound on the dimension of arbitrary correlation immune functions. We prove that such colorings with parameters $(x,12-x,4+x,8-x)$ exist if $x=0,2,3$ and do not exist if $x=1$.

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Document Type: Article
UDC: 519.172.2
MSC: 05С15
Received May 15, 2007, published June 29, 2007

Citation: D. G. Fon-Der-Flaass, “Perfect colorings of the $12$-cube that attain the bound on correlation immunity”, Sib. Èlektron. Mat. Izv., 4 (2007), 292–295

Citation in format AMSBIB
\by D.~G.~Fon-Der-Flaass
\paper Perfect colorings of the $12$-cube that attain the bound on correlation immunity
\jour Sib. \`Elektron. Mat. Izv.
\yr 2007
\vol 4
\pages 292--295

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    This publication is cited in the following articles:
    1. D. S. Krotov, “O sovershennykh raskraskakh polovinnogo 24-kuba”, Diskretn. analiz i issled. oper., 15:5 (2008), 35–46  mathnet  mathscinet  zmath
    2. D. B. Khoroshilova, “O tsirkulyarnykh sovershennykh raskraskakh v dva tsveta”, Diskretn. analiz i issled. oper., 16:1 (2009), 80–92  mathnet  mathscinet  zmath
    3. S. V. Avgustinovich, I. Yu. Mogilnykh, “Perfect 2-colorings of Johnson graphs $J(8,3)$ and $J(8,4)$”, J. Appl. Industr. Math., 5:1 (2011), 19–30  mathnet  crossref  mathscinet  zmath
    4. K. V. Vorobev, D. G. Fon-der-Flaass, “O sovershennykh $2$-raskraskakh giperkuba”, Sib. elektron. matem. izv., 7 (2010), 65–75  mathnet  mathscinet
    5. V. N. Potapov, “O sovershennykh raskraskakh buleva $n$-kuba i korrelyatsionno-immunnykh funktsiyakh maloi plotnosti”, Sib. elektron. matem. izv., 7 (2010), 372–382  mathnet
    6. Borges J., Rifà J., Zinoviev V.A., “On $q$-ary linear completely regular codes with $\rho=2$ and antipodal dual”, Adv. Math. Commun., 4:4 (2010), 567–578  crossref  mathscinet  zmath  isi  elib
    7. S. A. Puzynina, “On periodicity of perfect colorings of the infinite hexagonal and triangular grids”, Siberian Math. J., 52:1 (2011), 91–104  mathnet  crossref  mathscinet  isi
    8. D. B. Khoroshilova, “O parametrakh sovershennykh 2-raskrasok tsirkulyantnykh grafov”, Diskretn. analiz i issled. oper., 18:6 (2011), 82–89  mathnet  mathscinet  zmath
    9. Krotov D.S., “On weight distributions of perfect colorings and completely regular codes”, Des. Codes Cryptogr., 61:3 (2011), 315–329  crossref  mathscinet  zmath  isi  elib
    10. V. N. Potapov, “O sovershennykh 2-raskraskakh $q$-znachnogo giperkuba”, PDM, 2011, prilozhenie № 4, 18–20  mathnet
    11. Potapov V.N., “On perfect 2-colorings of the $q$-ary $n$-cube”, Discrete Math., 312:6 (2012), 1269–1272  crossref  mathscinet  zmath  isi  elib
    12. K. V. Vorobev, “Kratnye sovershennye kody v giperkube”, Diskretn. analiz i issled. oper., 19:4 (2012), 60–65  mathnet  mathscinet
    13. Borges J., Rifa J., Zinoviev V., “New Families of Completely Regular Codes and their Corresponding Distance Regular Coset Graphs”, Des. Codes Cryptogr., 70:1-2, SI (2014), 139–148  crossref  mathscinet  zmath  isi  elib
    14. Krotov D.S., “on Calculation of the Interweight Distribution of An Equitable Partition”, J. Algebr. Comb., 40:2 (2014), 373–386  crossref  mathscinet  zmath  isi  elib
    15. A. V. Khalyavin, M. S. Lobanov, Yu. V. Tarannikov, “On plateaued Boolean functions with the same spectrum support”, Sib. elektron. matem. izv., 13 (2016), 1346–1368  mathnet  crossref
    16. Alaeiyan M.H. Karami H., “Perfect 2-Colorings of the Platonic Graphs”, Int. J. Nonlinear Anal. Appl., 8:2 (2017), 29–35  crossref  zmath  isi
    17. Alaeiyan M. Mehrabani A., “Perfect 3-Colorings of the Cubic Graphs of Order 10”, Electron. J. Graph Theory Appl., 5:2 (2017), 194–206  crossref  mathscinet  isi  scopus
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