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Problemy Peredachi Informatsii, 2016, Volume 52, Issue 3, Pages 73–83
(Mi ppi2212)
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This article is cited in 2 scientific papers (total in 2 papers)
Coding Theory
On the symmetry group of the Mollard code
I. Yu. Mogilnykh, F. I. Solov'eva Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
Abstract:
We study the symmetry group of a binary perfect Mollard code $M(C,D)$ of length $tm+t+m$ containing as its subcodes the codes $C^1$ and $D^2$ formed from perfect codes $C$ and $D$ of lengths $t$ and $m$, respectively, by adding an appropriate number of zeros. For the Mollard codes, we generalize the result obtained in [1] for the symmetry group of Vasil'ev codes; namely, we describe the stabilizer $\mathrm{Stab}_{D^2}\mathrm{Sym}(M(C,D))$ of the subcode $D^2$ in the symmetry group of the code $M(C,D)$ (with the trivial function). Thus we obtain a new lower bound on the order of the symmetry group of the Mollard code. A similar result is established for the automorphism group of Steiner triple systems obtained by the Mollard construction but not necessarily associated with perfect codes. To obtain this result, we essentially use the notions of “linearity” of coordinate positions (points) of a nonlinear perfect code and a nonprojective Steiner triple system.
Received: 04.08.2015 Revised: 01.02.2016
Citation:
I. Yu. Mogilnykh, F. I. Solov'eva, “On the symmetry group of the Mollard code”, Probl. Peredachi Inf., 52:3 (2016), 73–83; Problems Inform. Transmission, 52:3 (2016), 265–275
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https://www.mathnet.ru/eng/ppi2212 https://www.mathnet.ru/eng/ppi/v52/i3/p73
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Abstract page: | 212 | Full-text PDF : | 41 | References: | 23 | First page: | 6 |
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