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Diskretn. Anal. Issled. Oper., Ser. 1, 2001, Volume 8, Number 4, Pages 3–8 (Mi da227)  

This article is cited in 9 scientific papers (total in 9 papers)

Perfect codes of complete rank with kernels of large dimensions

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: We construct perfect codes of all admissible lengths $n>20^{10}-1$ of complete rank with kernels of all possible dimensions $K$ from $(n-1)/2$ to $U(n)$, which is the maximum possible. For every $k\in \{(n-1)/2,…,U(n)-2\}$, we construct such codes of length $n,31\leqslant n\leqslant 2^{10}-1$.

Full text: PDF file (586 kB)

Bibliographic databases:
UDC: 519.72
Received: 25.07.2001

Citation: S. V. Avgustinovich, F. I. Solov'eva, O. Heden, “Perfect codes of complete rank with kernels of large dimensions”, Diskretn. Anal. Issled. Oper., Ser. 1, 8:4 (2001), 3–8

Citation in format AMSBIB
\Bibitem{AvgSolHed01}
\by S.~V.~Avgustinovich, F.~I.~Solov'eva, O.~Heden
\paper Perfect codes of complete rank with kernels of large dimensions
\jour Diskretn. Anal. Issled. Oper., Ser.~1
\yr 2001
\vol 8
\issue 4
\pages 3--8
\mathnet{http://mi.mathnet.ru/da227}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1918257}
\zmath{https://zbmath.org/?q=an:1003.94037}


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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. V. Avgustinovich, F. I. Solov'eva, O. Heden, “On the Rank and Kernel Problem for Perfect Codes”, Problems Inform. Transmission, 39:4 (2003), 341–345  mathnet  crossref  mathscinet  zmath
    2. 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
    3. 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
    4. S. A. Malyugin, “On enumeration of nonequivalent perfect binary codes of length 15 and rank 15”, J. Appl. Industr. Math., 1:1 (2007), 77–89  mathnet  crossref  mathscinet  zmath
    5. Heden O., “A remark on full rank perfect codes”, Discrete Math, 306:16 (2006), 1975–1980  crossref  mathscinet  zmath  isi  scopus
    6. Heden O., “A full rank perfect code of length 31”, Des Codes Cryptogr, 38:1 (2006), 125–129  crossref  mathscinet  zmath  isi  scopus
    7. Heden O., “A survey of perfect codes”, Adv Math Commun, 2:2 (2008), 223–247  crossref  mathscinet  zmath  isi  elib  scopus
    8. Solov'eva F.I., “On perfect binary codes”, Discrete Appl Math, 156:9 (2008), 1488–1498  crossref  mathscinet  zmath  isi  scopus
    9. Heden O., “Full rank perfect codes and alpha-kernels”, Discrete Math, 309:8 (2009), 2202–2216  crossref  mathscinet  zmath  isi  elib  scopus
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