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

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

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
\Bibitem{ZinRif07} \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} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000255782600003} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34547395766} `

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
2. Borges J., Rifà J., Zinoviev V. A., “On non-antipodal binary completely regular codes”, Discrete Math., 308:16 (2008), 3508–3525
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
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
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
6. Hyun J.Y., “A bound on equitable partitions of the Hamming space”, IEEE Trans. Inform. Theory, 56:5 (2010), 2109–2111
7. Rifà J., Zinoviev V.A., “On lifting perfect codes”, IEEE Trans. Inform. Theory, 57:9 (2011), 5918–5925
8. Krotov D.S., “On weight distributions of perfect colorings and completely regular codes”, Des. Codes Cryptogr., 61:3 (2011), 315–329
9. V. N. Potapov, “On the multidimensional permanent and $q$-ary designs”, Sib. elektron. matem. izv., 11 (2014), 451–456
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
11. Borges J. Rifa J. Zinoviev V., “Completely Regular Codes By Concatenating Hamming Codes”, Adv. Math. Commun., 12:2 (2018), 337–349
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