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Probl. Peredachi Inf., 2010, Volume 46, Issue 1, Pages 9–19 (Mi ppi2006)  

This article is cited in 2 scientific papers (total in 2 papers)

Coding Theory

On volumes of spheres for the stem distance

A. N. Voronina

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: For any two $q$-ary sequences $x$ and $y$, the stem similarity between them is defined as a total number of stems (blocks of length 2 consisting of adjacent elements of $x$ and $y$) in their longest common Hamming subsequence. For $q=4$ this similarity function and the corresponding distance function arise in molecular biology in describing an additive mathematical model of thermodynamic distance between DNA sequences. In the present paper, we derive explicit formulas for sphere sizes in this metric and consider their asymptotics in the case of spheres of a constant radius. Based on these results, we also obtain a random coding bound and Hamming bound for the optimal size of the so-called DNA codes for the case of a constant distance.

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English version:
Problems of Information Transmission, 2010, 46:1, 7–16

Bibliographic databases:

UDC: 621.391.15
Received: 03.09.2009
Revised: 14.01.2010

Citation: A. N. Voronina, “On volumes of spheres for the stem distance”, Probl. Peredachi Inf., 46:1 (2010), 9–19; Problems Inform. Transmission, 46:1 (2010), 7–16

Citation in format AMSBIB
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\by A.~N.~Voronina
\paper On volumes of spheres for the stem distance
\jour Probl. Peredachi Inf.
\yr 2010
\vol 46
\issue 1
\pages 9--19
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\transl
\jour Problems Inform. Transmission
\yr 2010
\vol 46
\issue 1
\pages 7--16
\crossref{https://doi.org/10.1134/S0032946010010023}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77951616670}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. S. Lebedev, “On enumeration of $q$-ary sequences with a fixed number of occurrences of the subblock 00”, Problems Inform. Transmission, 46:4 (2010), 376–381  mathnet  crossref  mathscinet  isi
    2. Dyachkov A., Volkova J., Polyanskii N., “DNA codes for generalized stem similarity”, 2011 IEEE International Symposium on Information Theory Proceedings (ISIT), 2011, 1564–1568  crossref  isi  scopus
  • Проблемы передачи информации Problems of Information Transmission
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