The isometry groups of the Hamming spaces of periodic sequences
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Date
2013
Authors
Oliynyk, Bogdana
Sushchanski, V.
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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.
Description
Keywords
Hamming space, Besicovitch space, isometry group, semidirect product, rooted tree, Bernoulli measure
Citation
Oliynyk B. The isometry groups of the Hamming spaces of periodic sequences / B. V. Oliynyk, V. I. Sushchanski // Siberian Mathematical Journal. - 2013. - Vol. 54, no. 1. - P. 124-136.