|
Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 1455–1462
(Mi semr1007)
|
|
|
|
Discrete mathematics and mathematical cybernetics
A note on regular subgroups of the automorphism group of the linear Hadamard code
I. Yu. Mogilnykhab a Sobolev Institute of Mathematics,
pr. Koptyuga, 4,
630090, Novosibirsk, Russia
b Tomsk State University, Regional Scientific and Educational Mathematical Center, pr. Lenina, 36, 634050, Tomsk, Russia
Abstract:
We consider the subgroups of the automorphism group of the linear Hadamard code that act regularly on the codewords of the code. These subgroups correspond to the regular subgroups of the general affine group $\mathrm{GA}(r,2)$ with respect to the action on the vectors of $F_2^{r}$, where $n=2^r-1 $ is the length of the Hamadard code. We show that the dihedral group $D_{2^{r-1}}$ is a regular subgroup of $\mathrm{GA}(r,2)$ only when $r=3$. Following the approach of [13] we study the regular subgroups of the automorphism group of the Hamming code obtained from the regular subgroups of the automorphism group of the Hadamard code of length $15$.
Keywords:
error-correcting code, automorphism group, regular action, affine group.
DOI:
https://doi.org/10.33048/semi.2018.15.119
Full text:
PDF file (149 kB)
References:
PDF file
HTML file
Bibliographic databases:
Document Type:
Article
UDC:
519.725
MSC: 94B60 Received July 12, 2018, published November 22, 2018
Language: English
Citation:
I. Yu. Mogilnykh, “A note on regular subgroups of the automorphism group of the linear Hadamard code”, Sib. Èlektron. Mat. Izv., 15 (2018), 1455–1462
Citation in format AMSBIB
\Bibitem{Mog18}
\by I.~Yu.~Mogilnykh
\paper A note on regular subgroups of the automorphism group of the linear Hadamard code
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 1455--1462
\mathnet{http://mi.mathnet.ru/semr1007}
\crossref{https://doi.org/10.33048/semi.2018.15.119}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000454860200061}
Linking options:
http://mi.mathnet.ru/eng/semr1007 http://mi.mathnet.ru/eng/semr/v15/p1455
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
|
Number of views: |
This page: | 11 | Full text: | 1 |
|