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The isometry groups of the hamming spaces of periodic sequences

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Abstract

We consider the Hamming space of periodic (0, 1)-sequences and a continual family of its subspaces defined as direct limits of finite Hamming spaces. These subspaces form a complete lattice under inclusion which is isomorphic to the lattice of supernatural numbers. We explicitly describe the isometry groups of these spaces. This involves certain constructions similar to the hyperoctahedral groups but accounting for additional structures on the underlying sets.

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Authors and Affiliations

  1. Taras Shevchenko Kiev National University, Kiev, Ukraine

    B. V. Oliynyk

  2. Silesian University of Technology, Gliwice, Poland

    V. I. Sushchanskiĭ

Authors
  1. B. V. Oliynyk
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  2. V. I. Sushchanskiĭ
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Correspondence to B. V. Oliynyk.

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Original Russian Text Copyright © 2013 Oliynyk B.V. and Sushchanskiĭ V.I.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 54, No. 1, pp. 163–179, January–February, 2013.

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Oliynyk, B.V., Sushchanskiĭ, V.I. The isometry groups of the hamming spaces of periodic sequences. Sib Math J 54, 124–136 (2013). https://doi.org/10.1134/S0037446613010163

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  • DOI: https://doi.org/10.1134/S0037446613010163

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