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.
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Original Russian Text © I.Yu. Mogilnykh, F.I. Solov’eva, 2015, published in Problemy Peredachi Informatsii, 2015, Vol. 51, No. 2, pp. 57–66.
The research was carried out at the expense of the Russian Science Foundation, project no. 14-11-00555.
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Mogilnykh, I.Y., Solov’eva, F.I. On separability of the classes of homogeneous and transitive perfect binary codes. Probl Inf Transm 51, 139–147 (2015). https://doi.org/10.1134/S0032946015020054
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DOI: https://doi.org/10.1134/S0032946015020054