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This article is cited in 4 scientific papers (total in 4 papers)
Discrete mathematics and mathematical cybernetics
A concatenation construction for propelinear perfect codes from regular subgroups of $\mathrm{GA}(r,2)$
I. Yu. Mogilnykhab, F. I. Solov'evaa a Sobolev Institute of Mathematics,
4, Koptyuga ave.,
Novosibirsk, 630090, Russia
b Tomsk State University,
Regional Scientific and Educational Mathematical Center,
36, Lenina ave.,
Tomsk, 634050, Russia
Abstract:
A code $C$ is called propelinear if there
is a subgroup of $\mathrm{Aut}(C)$ of order $|C|$ acting transitively on the
codewords of $C$. In the paper new propelinear perfect binary codes
of any admissible length more than $7$ are obtained by a particular
case of the Solov'eva concatenation construction–1981 and the
regular subgroups of the general affine group
of the vector space over $\mathrm{GF}(2)$.
Keywords:
Hamming code, perfect code, concatenation construction, propelinear code, Mollard code, regular subgroup, transitive action.
Received March 15, 2019, published November 21, 2019
Citation:
I. Yu. Mogilnykh, F. I. Solov'eva, “A concatenation construction for propelinear perfect codes from regular subgroups of $\mathrm{GA}(r,2)$”, Sib. Èlektron. Mat. Izv., 16 (2019), 1689–1702
Linking options:
https://www.mathnet.ru/eng/semr1160 https://www.mathnet.ru/eng/semr/v16/p1689
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