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Probl. Peredachi Inf., 2005, Volume 41, Issue 2, Pages 42–49 (Mi ppi94)  

This article is cited in 13 scientific papers (total in 13 papers)

Coding Theory

On the Structure of Symmetry Groups of Vasil'ev Codes

S. V. Avgustinovicha, F. I. Solov'evaa, O. Hedenb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Royal Institute of Technology

Abstract: The structure of symmetry groups of Vasil'ev codes is studied. It is proved that the symmetry group of an arbitrary perfect binary non-full-rank Vasil'ev code of length $n$ is always nontrivial; for codes of rank $n-\log(n+1)+1$, an attainable upper bound on the order of the symmetry group is obtained.

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English version:
Problems of Information Transmission, 2005, 41:2, 105–112

Bibliographic databases:

UDC: 621.391.15
Received: 22.09.2004

Citation: S. V. Avgustinovich, F. I. Solov'eva, O. Heden, “On the Structure of Symmetry Groups of Vasil'ev Codes”, Probl. Peredachi Inf., 41:2 (2005), 42–49; Problems Inform. Transmission, 41:2 (2005), 105–112

Citation in format AMSBIB
\by S.~V.~Avgustinovich, F.~I.~Solov'eva, O.~Heden
\paper On the Structure of Symmetry Groups
of Vasil'ev Codes
\jour Probl. Peredachi Inf.
\yr 2005
\vol 41
\issue 2
\pages 42--49
\jour Problems Inform. Transmission
\yr 2005
\vol 41
\issue 2
\pages 105--112

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    This publication is cited in the following articles:
    1. Solov'eva F.I., “On perfect binary codes”, Discrete Appl. Math., 156:9 (2008), 1488–1498  crossref  mathscinet  zmath  isi
    2. 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
    3. Heden O., Pasticci F., Westerbäck Th., “On the existence of extended perfect binary codes with trivial symmetry group”, Adv. Math. Commun., 3:3 (2009), 295–309  crossref  mathscinet  zmath  isi  elib
    4. E. V. Gorkunov, “Monomialnye avtomorfizmy lineinoi i prostoi komponent koda Khemminga”, Diskretn. analiz i issled. oper., 17:1 (2010), 11–33  mathnet  mathscinet  zmath
    5. 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
    6. 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
    7. 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
    8. Heden O., Pasticci F., Westerback T., “On the Symmetry Group of Extended Perfect Binary Codes of Length N+1 and Rank N-Log(N+1)+2”, Adv. Math. Commun., 6:2 (2012), 121–130  crossref  mathscinet  zmath  isi  elib
    9. Phelps K.T., “Involutions in Additive 3-Perfect Codes”, IEEE Trans. Inf. Theory, 59:10 (2013), 6593–6596  crossref  mathscinet  isi  elib
    10. I. Yu. Mogilnykh, F. I. Solov'eva, “On separability of the classes of homogeneous and transitive perfect binary codes”, Problems Inform. Transmission, 51:2 (2015), 139–147  mathnet  crossref  isi  elib
    11. Mogilnykh I.Yu., Solov'eva F.I., “Transitive Nonpropelinear Perfect Codes”, Discrete Math., 338:3 (2015), 174–182  crossref  mathscinet  zmath  isi  elib
    12. Krotov D.S., Villanueva M., “Classification of the Z(2)Z(4)-Linear Hadamard Codes and Their Automorphism Groups”, IEEE Trans. Inf. Theory, 61:2 (2015), 887–894  crossref  mathscinet  isi  elib
    13. 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
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