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Problemy Peredachi Informatsii, 2015, Volume 51, Issue 2, Pages 57–66
(Mi ppi2170)
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This article is cited in 1 scientific paper (total in 1 paper)
Coding Theory
On separability of the classes of homogeneous and transitive perfect binary codes
I. Yu. Mogilnykhab, F. I. Solov'evaab a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
Abstract:
By the example of perfect binary codes, we prove the existence of binary homogeneous nontransitive codes. Thereby, taking into account previously obtained results, we establish a hierarchical picture of extents of linearity for binary codes; namely, there is a strict inclusion of the class of binary linear codes in the class of binary propelinear codes, which are strictly included in the class of binary transitive codes, which, in turn, are strictly included in the class of binary homogeneous codes. We derive a transitivity criterion for perfect binary codes of rank greater by one than the rank of the Hamming code of the same length.
Received: 09.12.2014 Revised: 19.02.2015
Citation:
I. Yu. Mogilnykh, F. I. Solov'eva, “On separability of the classes of homogeneous and transitive perfect binary codes”, Probl. Peredachi Inf., 51:2 (2015), 57–66; Problems Inform. Transmission, 51:2 (2015), 139–147
Linking options:
https://www.mathnet.ru/eng/ppi2170 https://www.mathnet.ru/eng/ppi/v51/i2/p57
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Abstract page: | 199 | Full-text PDF : | 45 | References: | 28 | First page: | 13 |
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