Geodesic
Error-Correcting Codes from k -Resolving Sets
Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 2, pp. 341-355

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We demonstrate a construction of error-correcting codes from graphs by means of k-resolving sets, and present a decoding algorithm which makes use of covering designs. Along the way, we determine the k-metric dimension of grid graphs (i.e., Cartesian products of paths).
Keywords: error-correcting code, k -resolving set, k -metric dimension, covering design, uncovering, grid graph 
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     author = {Bailey, Robert F. and Yero, Ismael G.},
     title = {Error-Correcting {Codes} from k {-Resolving} {Sets}},
     journal = {Discussiones Mathematicae. Graph Theory},
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     publisher = {mathdoc},
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     year = {2019},
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Bailey, Robert F.; Yero, Ismael G. Error-Correcting Codes from k -Resolving Sets. Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 2, pp. 341-355. http://geodesic.mathdoc.fr/item/DMGT_2019_39_2_a3/