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Problemy Peredachi Informatsii, 2017, Volume 53, Issue 3, Pages 54–63
(Mi ppi2243)
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This article is cited in 1 scientific paper (total in 1 paper)
Coding Theory
Propelinear codes related to some classes of optimal codes
I. Yu. Mogilnykh, F. I. Solov'eva 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 that acts regularly on codewords. We show propelinearity of complements of cyclic codes $C_{1,i}$, $(i,2^m-1)=1$, of length $n=2^m-1$, including the primitive two-error-correcting BCH code, to the Hamming code; the Preparata code to the Hamming code; the Goethals code to the Preparata code; and the $\mathbb Z_4$-linear Preparata code to the $\mathbb Z_4$-linear perfect code.
Received: 08.11.2016 Revised: 28.04.2017
Citation:
I. Yu. Mogilnykh, F. I. Solov'eva, “Propelinear codes related to some classes of optimal codes”, Probl. Peredachi Inf., 53:3 (2017), 54–63; Problems Inform. Transmission, 53:3 (2017), 251–259
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https://www.mathnet.ru/eng/ppi2243 https://www.mathnet.ru/eng/ppi/v53/i3/p54
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Abstract page: | 201 | Full-text PDF : | 33 | References: | 32 | First page: | 17 |
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