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Probl. Peredachi Inf., 2016, Volume 52, Issue 3, Pages 97–107 (Mi ppi2215)  

This article is cited in 2 scientific papers (total in 2 papers)

Coding Theory

On extending propelinear structures of the Nordstrom–Robinson code to the Hamming code

I. Yu. Mogil'nykh

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

Abstract: A code is said to be propelinear if its automorphism group contains a subgroup which acts on the codewords regularly. Such a subgroup is called a propelinear structure on the code. With the aid of computer, we enumerate all propelinear structures on the Nordstrom–Robinson code and analyze the problem of extending them to propelinear structures on the extended Hamming code of length 16. The latter result is based on the description of partitions of the Hamming code of length 16 into Nordstrom–Robinson codes via Fano planes, presented in the paper. As a result, we obtain a record-breaking number of propelinear structures in the class of extended perfect codes of length 16.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00463а
Russian Science Foundation 14-11-00555
The results of Section 3 of the paper are obtained under the support of the Russian Foundation for Basic Research, project no. 13-01-00463; results of Section 4 are funded by the Russian Science Foundation, project no. 14-11-00555.


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English version:
Problems of Information Transmission, 2016, 52:3, 289–298

Bibliographic databases:

UDC: 621.391.15
Received: 08.09.2015
Revised: 24.05.2016

Citation: I. Yu. Mogil'nykh, “On extending propelinear structures of the Nordstrom–Robinson code to the Hamming code”, Probl. Peredachi Inf., 52:3 (2016), 97–107; Problems Inform. Transmission, 52:3 (2016), 289–298

Citation in format AMSBIB
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\by I.~Yu.~Mogil'nykh
\paper On extending propelinear structures of the Nordstrom--Robinson code to the Hamming code
\jour Probl. Peredachi Inf.
\yr 2016
\vol 52
\issue 3
\pages 97--107
\mathnet{http://mi.mathnet.ru/ppi2215}
\elib{http://elibrary.ru/item.asp?id=27577369}
\transl
\jour Problems Inform. Transmission
\yr 2016
\vol 52
\issue 3
\pages 289--298
\crossref{https://doi.org/10.1134/S0032946016030078}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84991698409}


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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. Mogilnykh, F. I. Solov'eva, “Propelinear codes related to some classes of optimal codes”, Problems Inform. Transmission, 53:3 (2017), 251–259  mathnet  crossref  isi  elib
    2. I. Yu. Mogilnykh, “A note on regular subgroups of the automorphism group of the linear Hadamard code”, Sib. elektron. matem. izv., 15 (2018), 1455–1462  mathnet  crossref
  • Проблемы передачи информации Problems of Information Transmission
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