Error-Correcting Codes from k-Resolving Sets

We demonstrate a construction of error-correcting codes from graphs by means of -resolving sets, and present a decoding algorithm which makes use of covering designs. Along the way, we determine the -metric dimension of grid graphs (i.e., Cartesian products of paths).

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Bibliographic Details
Published inDiscussiones Mathematicae. Graph Theory Vol. 39; no. 2; pp. 341 - 355
Main Authors Bailey, Robert F., Yero, Ismael G.
Format Journal Article
LanguageEnglish
Published Sciendo 01.01.2019
University of Zielona Góra
Subjects
05B40
05C12
94B25
94B35
covering design
error-correcting code
grid graph
k-metric dimension
k-resolving set
metric dimension
resolving set
uncovering
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Summary:We demonstrate a construction of error-correcting codes from graphs by means of -resolving sets, and present a decoding algorithm which makes use of covering designs. Along the way, we determine the -metric dimension of grid graphs (i.e., Cartesian products of paths).
ISSN:1234-3099
2083-5892
DOI:10.7151/dmgt.2087