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Probl. Peredachi Inf., 2007, Volume 43, Issue 2, Pages 34–51 (Mi ppi10)  

This article is cited in 11 scientific papers (total in 11 papers)

Coding Theory

On New Completely Regular $q$-ary Codes

V. A. Zinov'eva, J. Rifàb

a A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences
b Universitat Autònoma de Barcelona

Abstract: In this paper, new completely regular $q$-ary codes are constructed from $q$-ary perfect codes. In particular, several new ternary completely regular codes are obtained from the ternary $[11,6,5]$ Golay code. One of these codes with parameters $[11,5,6]$ has covering radius $\rho=5$ and intersection array $(22,20,18,2,1;1,2,9,20,22)$. This code is dual to the ternary perfect $[11,6,5]$ Golay code. Another $[10,5,5]$ code has covering radius $\rho=4$ and intersection array $(20,18,4,1;1,2,18,20)$. This code is obtained by deleting one position of the former code. All together, the ternary Golay code results in eight completely regular codes, only four of which were previously known. Also, new infinite families of completely regular codes are constructed from $q$-ary Hamming codes.

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English version:
Problems of Information Transmission, 2007, 43:2, 97–112

Bibliographic databases:

UDC: 621.391.15
Received: 24.08.2006

Citation: V. A. Zinov'ev, J. Rifà, “On New Completely Regular $q$-ary Codes”, Probl. Peredachi Inf., 43:2 (2007), 34–51; Problems Inform. Transmission, 43:2 (2007), 97–112

Citation in format AMSBIB
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\by V.~A.~Zinov'ev, J.~Rif\`a
\paper On New Completely Regular $q$-ary Codes
\jour Probl. Peredachi Inf.
\yr 2007
\vol 43
\issue 2
\pages 34--51
\mathnet{http://mi.mathnet.ru/ppi10}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2333855}
\transl
\jour Problems Inform. Transmission
\yr 2007
\vol 43
\issue 2
\pages 97--112
\crossref{https://doi.org/10.1134/S0032946007020032}
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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. I. Yu. Mogil'nykh, “On the Regularity of Perfect Two-Colorings of the Johnson Graph”, Problems Inform. Transmission, 43:4 (2007), 303–309  mathnet  crossref  mathscinet  zmath  isi
    2. Borges J., Rifà J., Zinoviev V. A., “On non-antipodal binary completely regular codes”, Discrete Math., 308:16 (2008), 3508–3525  crossref  mathscinet  zmath  isi  elib
    3. Avgustinovich S., Mogilnykh I., “Perfect 2-colorings of Johnson graphs J(6,3) and J(7,3)”, Coding theory and applications, Proceedings, Lecture Notes in Comput. Sci., 5228, 2008, 11–19  crossref  mathscinet  zmath  isi
    4. Rifà J., Zinoviev V.A., “On a class of binary linear completely transitive codes with arbitrary covering radius”, Discrete Math., 309:16 (2009), 5011–5016  crossref  mathscinet  zmath  isi  elib
    5. Borges J., Rifà J., Zinoviev V.A., “On $q$-ary linear completely regular codes with $\rho=2$ and antipodal dual”, Adv. Math. Commun., 4:4 (2010), 567–578  crossref  mathscinet  zmath  isi  elib
    6. Hyun J.Y., “A bound on equitable partitions of the Hamming space”, IEEE Trans. Inform. Theory, 56:5 (2010), 2109–2111  crossref  mathscinet  isi  elib
    7. Rifà J., Zinoviev V.A., “On lifting perfect codes”, IEEE Trans. Inform. Theory, 57:9 (2011), 5918–5925  crossref  mathscinet  isi  elib
    8. Krotov D.S., “On weight distributions of perfect colorings and completely regular codes”, Des. Codes Cryptogr., 61:3 (2011), 315–329  crossref  mathscinet  zmath  isi  elib
    9. V. N. Potapov, “On the multidimensional permanent and $q$-ary designs”, Sib. elektron. matem. izv., 11 (2014), 451–456  mathnet
    10. Borges J. Rifa J. Zinoviev V., “New Families of Completely Regular Codes and Their Corresponding Distance Regular Coset Graphs”, Des. Codes Cryptogr., 70:1-2, SI (2014), 139–148  crossref  mathscinet  zmath  isi  elib
    11. Borges J. Rifa J. Zinoviev V., “Completely Regular Codes By Concatenating Hamming Codes”, Adv. Math. Commun., 12:2 (2018), 337–349  crossref  mathscinet  zmath  isi  scopus
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