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arXiv · 1412.3006

On homogeneous nontransitive binary perfect code

I. Yu. Mogilnykh·F. I. Solov'eva
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Abstract

Studying binary perfect codes we show the existence of homogeneous nontransitive codes. Thus, as far as perfect codes are concerned, the propelinear codes are strictly contained in transitive codes, wheresas homogeneous codes form a strict subclass of transitive codes. In the work we deduce a necessary and sufficient condition for transitivity of perfect binary codes of rank one more than that of Hamming code. The paper is in Russian.

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I. Yu. Mogilnykh, F. I. Solov'eva. 2014-12-09. On homogeneous nontransitive binary perfect code. https://arxiv.org/abs/1412.3006

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