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Problemy Peredachi Informatsii, 2000, Volume 36, Issue 4, Pages 53–58 (Mi ppi494)  
This article is cited in 16 scientific papers (total in 16 papers)

Coding Theory

On Automorphism Groups of Perfect Binary Codes and Steiner Triple Systems

F. I. Solov'eva, S. T. Topalova
Full-text PDF (691 kB) Citations (16)
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Abstract: We prove that the order of the automorphism group of an arbitrary perfect binary code with $d=3$ is not greater than that of the automorphism group of the Hamming code of the same length. We also obtain an upper estimate for the order of the automorphism group of an arbitrary Steiner system $S(t,t+1,n)$.
Received: 21.02.2000
Revised: 26.07.2000
Bibliographic databases:
Document Type: Article
UDC: 621.391.15
Language: Russian
Citation: F. I. Solov'eva, S. T. Topalova, “On Automorphism Groups of Perfect Binary Codes and Steiner Triple Systems”, Probl. Peredachi Inf., 36:4 (2000), 53–58; Problems Inform. Transmission, 36:4 (2000), 331–335
Citation in format AMSBIB
\Bibitem{SolTop00}
\by F.~I.~Solov'eva, S.~T.~Topalova
\paper On Automorphism Groups of Perfect Binary Codes and Steiner Triple Systems
\jour Probl. Peredachi Inf.
\yr 2000
\vol 36
\issue 4
\pages 53--58
\mathnet{http://mi.mathnet.ru/ppi494}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1813652}
\zmath{https://zbmath.org/?q=an:0984.94035}
\transl
\jour Problems Inform. Transmission
\yr 2000
\vol 36
\issue 4
\pages 331--335
Linking options:
  • https://www.mathnet.ru/eng/ppi494
  • https://www.mathnet.ru/eng/ppi/v36/i4/p53
    • This publication is cited in the following 16 articles:
    1. Falcone G. Pavone M., “Binary Hamming Codes and Boolean Designs”, Designs Codes Cryptogr., 89:6 (2021), 1261–1277  crossref  mathscinet  zmath  isi  scopus
    2. Shi M., Xu L., Krotov D.S., “on the Number of Resolvable Steiner Triple Systems of Small 3-Rank”, Designs Codes Cryptogr., 88:6 (2020), 1037–1046  crossref  mathscinet  zmath  isi  scopus
    3. I. Yu. Mogilnykh, “A note on regular subgroups of the automorphism group of the linear Hadamard code”, Sib. elektron. matem. izv., 15 (2018), 1455–1462  mathnet  crossref
    4. I. Yu. Mogilnykh, F. I. Solov'eva, “On the symmetry group of the Mollard code”, Problems Inform. Transmission, 52:3 (2016), 265–275  mathnet  crossref  isi  elib
    5. I. Yu. Mogil'nykh, “On extending propelinear structures of the Nordstrom–Robinson code to the Hamming code”, Problems Inform. Transmission, 52:3 (2016), 289–298  mathnet  crossref  isi  elib
    6. Heden O., “A Note on the Symmetry Group of Full Rank Perfect Binary Codes”, Discrete Math., 312:19 (2012), 2973–2977  crossref  mathscinet  zmath  isi  elib
    7. Borges J. Mogilnykh I.Yu. Rifa J. Solov'eva F.I., “Structural Properties of Binary Propelinear Codes”, Adv. Math. Commun., 6:3 (2012), 329–346  crossref  mathscinet  zmath  isi  elib
    8. Fernandez-Cordoba C., Phelps K.T., Villanueva M., “Involutions in Binary Perfect Codes”, IEEE Trans Inform Theory, 57:9 (2011), 5926–5932  crossref  mathscinet  isi  elib
    9. Heden O., “On the size of the symmetry group of a perfect code”, Discrete Math, 311:17 (2011), 1879–1885  crossref  mathscinet  zmath  isi  elib
    10. E. V. Gorkunov, “Monomialnye avtomorfizmy lineinoi i prostoi komponent koda Khemminga”, Diskretn. analiz i issled. oper., 17:1 (2010), 11–33  mathnet  mathscinet  zmath
    11. E. V. Gorkunov, “The group of permutational automorphisms of a $q$-ary Hamming code”, Problems Inform. Transmission, 45:4 (2009), 309–316  mathnet  crossref  mathscinet  zmath  isi
    12. Heden, O, “ON THE EXISTENCE OF EXTENDED PERFECT BINARY CODES WITH TRIVIAL SYMMETRY GROUP”, Advances in Mathematics of Communications, 3:3 (2009), 295  crossref  mathscinet  zmath  isi
    13. Heden, O, “A survey of perfect codes”, Advances in Mathematics of Communications, 2:2 (2008), 223  crossref  mathscinet  zmath  isi
    14. Solov'eva, FI, “On perfect binary codes”, Discrete Applied Mathematics, 156:9 (2008), 1488  crossref  mathscinet  zmath  isi
    15. S. V. Avgustinovich, F. I. Solov'eva, O. Heden, “On the Structure of Symmetry Groups of Vasil'ev Codes”, Problems Inform. Transmission, 41:2 (2005), 105–112  mathnet  crossref  mathscinet  zmath
    16. Phelps, KT, “On binary 1-perfect additive codes: Some structural properties”, IEEE Transactions on Information Theory, 48:9 (2002), 2587  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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