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Probl. Peredachi Inf., 2006, Volume 42, Issue 2, Pages 63–80 (Mi ppi45)  

This article is cited in 10 scientific papers (total in 10 papers)

Coding Theory

Binary Extended Perfect Codes of Length 16 and Rank 14

V. A. Zinov'ev, D. V. Zinov'ev

Institute for Information Transmission Problems, Russian Academy of Sciences

Abstract: All extended binary perfect $(16,4,2^11)$ codes of rank 14 over the field $\mathbb F_2$ are classified. It is proved that among all nonequivalent extended binary perfect $(16,4,2^11)$ codes there are exactly 1719 nonequivalent codes of rank 14 over $\mathbb F_2$. Among these codes there are 844 codes classified by Phelps (Solov?eva–Phelps codes) and 875 other codes obtained by the construction of Etzion–Vardy and by a new general doubling construction, presented in the paper. Thus, the only open question in the classification of extended binary perfect $(16,4,2^11)$ codes is that on such codes of rank 15 over $\mathbb F_2$.

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English version:
Problems of Information Transmission, 2006, 42:2, 123–138

Bibliographic databases:

UDC: 621.391.15
Received: 11.01.2005
Revised: 02.03.2006

Citation: V. A. Zinov'ev, D. V. Zinov'ev, “Binary Extended Perfect Codes of Length 16 and Rank 14”, Probl. Peredachi Inf., 42:2 (2006), 63–80; Problems Inform. Transmission, 42:2 (2006), 123–138

Citation in format AMSBIB
\by V.~A.~Zinov'ev, D.~V.~Zinov'ev
\paper Binary Extended Perfect Codes of Length~16 and Rank~14
\jour Probl. Peredachi Inf.
\yr 2006
\vol 42
\issue 2
\pages 63--80
\jour Problems Inform. Transmission
\yr 2006
\vol 42
\issue 2
\pages 123--138

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    This publication is cited in the following articles:
    1. V. A. Zinov'ev, D. V. Zinov'ev, “Classification of Steiner Quadruple Systems of Order 16 and of Rank 14”, Problems Inform. Transmission, 42:3 (2006), 217–229  mathnet  crossref  mathscinet
    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., “The partial order of perfect codes associated to a perfect code”, Adv. Math. Commun., 1:4 (2007), 399–412  crossref  mathscinet  zmath  isi
    4. Yu. L. Vasil'ev, S. V. Avgustinovich, D. S. Krotov, “On mobile sets in the binary hypercube”, J. Appl. Industr. Math., 3:2 (2009), 290–296  mathnet  crossref  mathscinet  zmath
    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. Heden O., “A survey of perfect codes”, Adv. Math. Commun., 2:2 (2008), 223–247  crossref  mathscinet  zmath  isi  elib
    7. Krotov D. S., Avgustinovich S. V., “On the number of 1-perfect binary codes: a lower bound”, IEEE Trans. Inform. Theory, 54:4 (2008), 1760–1765  crossref  mathscinet  zmath  isi  elib
    8. V. A. Zinoviev, D. V. Zinoviev, “Binary perfect and extended perfect codes of lengths 15 and 16 with ranks 13 and 14”, Problems Inform. Transmission, 46:1 (2010), 17–21  mathnet  crossref  mathscinet  isi
    9. Östergård P.R.J., Pottonen O., Phelps K.T., “The perfect binary one-error-correcting codes of length 15: Part II—properties”, IEEE Trans. Inform. Theory, 56:6 (2010), 2571–2582  crossref  mathscinet  isi
    10. Heden O., Hessler M., Westerbäck T., “On the classification of perfect codes: extended side class structures”, Discrete Math., 310:1 (2010), 43–55  crossref  mathscinet  zmath  isi  elib
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