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Probl. Peredachi Inf., 2003, Volume 39, Issue 4, Pages 30–34 (Mi ppi313)  

This article is cited in 15 scientific papers (total in 15 papers)

Information Theory and Coding Theory

On the Rank and Kernel Problem for Perfect 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: A construction is proposed which, for $n$ large enough, allows one to build perfect binary codes of length $n$ and rank $r$, with kernel of dimension $k$, for any admissible pair $(r,k)$ within the limits of known bounds.

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English version:
Problems of Information Transmission, 2003, 39:4, 341–345

Bibliographic databases:

UDC: 621.391.15
Received: 20.01.2003

Citation: S. V. Avgustinovich, F. I. Solov'eva, O. Heden, “On the Rank and Kernel Problem for Perfect Codes”, Probl. Peredachi Inf., 39:4 (2003), 30–34; Problems Inform. Transmission, 39:4 (2003), 341–345

Citation in format AMSBIB
\by S.~V.~Avgustinovich, F.~I.~Solov'eva, O.~Heden
\paper On the Rank and Kernel Problem for Perfect Codes
\jour Probl. Peredachi Inf.
\yr 2003
\vol 39
\issue 4
\pages 30--34
\jour Problems Inform. Transmission
\yr 2003
\vol 39
\issue 4
\pages 341--345

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    This publication is cited in the following articles:
    1. 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
    2. A. M. Romanov, “A survey of methods for constructing nonlinear perfect binary codes”, J. Appl. Industr. Math., 2:2 (2008), 252–269  mathnet  crossref  mathscinet  zmath
    3. Heden O., Hessler M., “On the classification of perfect codes: side class structures”, Des. Codes Cryptogr., 40:3 (2006), 319–333  crossref  mathscinet  zmath  isi
    4. Heden O., “Perfect codes from the dual point of view. I”, Discrete Math., 308:24 (2008), 6141–6156  crossref  mathscinet  zmath  isi
    5. Heden O., “Perfect codes of length $n$ with kernels of dimension $n-\log(n+1)-3$”, SIAM J. Discrete Math., 22:4 (2008), 1338–1350  crossref  mathscinet  zmath  isi  elib
    6. Popescu D.C., “The algebraic degree of perfect binary codes”, IEEE Trans. Inform. Theory, 54:11 (2008), 5198–5202  crossref  mathscinet  zmath  isi  elib
    7. Heden O., “A survey of perfect codes”, Adv. Math. Commun., 2:2 (2008), 223–247  crossref  mathscinet  zmath  isi  elib
    8. Solov'eva F.I., “On perfect binary codes”, Discrete Appl. Math., 156:9 (2008), 1488–1498  crossref  mathscinet  zmath  isi
    9. Pasticci F., Westerbäck Th., “On rank and kernel of some mixed perfect codes”, Discrete Math., 309:9 (2009), 2763–2774  crossref  mathscinet  zmath  isi  elib
    10. 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
    11. Avgustinovich S.V., Krotov D.S., “Embedding in a perfect code”, J. Combin. Des., 17:5 (2009), 419–423  crossref  mathscinet  zmath  isi
    12. Heden O., “Full rank perfect codes and alpha-kernels”, Discrete Math, 309:8 (2009), 2202–2216  crossref  mathscinet  zmath  isi  elib
    13. Heden O., Hessler M., Westerback T., “On the classification of perfect codes: Extended side class structures”, Discrete Math, 310:1 (2010), 43–55  crossref  mathscinet  zmath  isi  elib
    14. 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
    15. D. I. Kovalevskaya, “Mollard code as a robust nonlinear code”, Problems Inform. Transmission, 54:1 (2018), 34–47  mathnet  crossref  isi  elib
  • Проблемы передачи информации Problems of Information Transmission
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