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JOURNALS // Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports] // Archive

Sib. Èlektron. Mat. Izv., 2019 Volume 16, Pages 1689–1702 (Mi semr1160)

This article is cited in 3 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.

UDC: 519.725

MSC: 94B60

Received March 15, 2019, published November 21, 2019

Language: English

DOI: 10.33048/semi.2019.16.119



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