This article is cited in 2 scientific papers (total in 2 papers)
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
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.
|Russian Foundation for Basic Research
|Russian Science Foundation
|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.
PDF file (215 kB)
Problems of Information Transmission, 2016, 52:3, 289–298
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
\paper On extending propelinear structures of the Nordstrom--Robinson code to the Hamming code
\jour Probl. Peredachi Inf.
\jour Problems Inform. Transmission
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
I. Yu. Mogilnykh, F. I. Solov'eva, “Propelinear codes related to some classes of optimal codes”, Problems Inform. Transmission, 53:3 (2017), 251–259
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
|Number of views:|