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Diskretn. Anal. Issled. Oper., 2008, Volume 15, Number 5, Pages 35–46 (Mi da548)  

This article is cited in 5 scientific papers (total in 5 papers)

On perfect colorings of the halved 24-cube

D. S. Krotov

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

Abstract: We consider perfect 2-colorings of the distance-2 graph of the 24-cube $\{0,1\}^{24}$ with parameters $((20+c,256-c)(c,276-c))$ (i.e., with the eigenvalue 20). We prove that such colorings exist for all $c$ from 1 to 128 except 1, 2, 4, 5, 7, 10, 13 and do not exist for $c=1,2,4,5,7$. Tabl. 2, bibl. 4.

Keywords: perfect coloring, equitable partition, halved $n$-cube.

Full text: PDF file (285 kB)
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Bibliographic databases:

UDC: 519.2+621.391
Received: 18.03.2008

Citation: D. S. Krotov, “On perfect colorings of the halved 24-cube”, Diskretn. Anal. Issled. Oper., 15:5 (2008), 35–46

Citation in format AMSBIB
\Bibitem{Kro08}
\by D.~S.~Krotov
\paper On perfect colorings of the halved 24-cube
\jour Diskretn. Anal. Issled. Oper.
\yr 2008
\vol 15
\issue 5
\pages 35--46
\mathnet{http://mi.mathnet.ru/da548}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2543153}
\zmath{https://zbmath.org/?q=an:1249.05122}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. S. V. Avgustinovich, M. A. Lisitsyna, “Perfect 2-colorings of transitive cubic graphs”, J. Appl. Industr. Math., 5:4 (2011), 519–528  mathnet  crossref  mathscinet  zmath
    3. S. V. Avgustinovich, A. Yu. Vasil'eva, I. V. Sergeeva, “Distance regular colorings of the infinite rectangular grid”, J. Appl. Industr. Math., 6:3 (2012), 280–285  mathnet  crossref  mathscinet  zmath
    4. 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  scopus
    5. K. V. Vorobëv, “Kratnye sovershennye kody v giperkube”, Diskretn. analiz i issled. oper., 19:4 (2012), 60–65  mathnet  mathscinet
  • Дискретный анализ и исследование операций
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