Error-correcting codes from k-resolving sets
Copyright policy )Error-correcting codes from k-resolving sets
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).
13 pages, 2 figures
05C12, 94B25, 05B40, 94B35, Decoding, Graph operations (line graphs, products, etc.), 94b35, k-resolving set, uncovering, error-correcting code, k-resolving set, covering design, QA1-939, FOS: Mathematics, Mathematics - Combinatorics, 05c12, uncovering, grid graph, Combinatorial aspects of packing and covering, \(k\)-resolving set, \(k\)-metric dimension, Combinatorial codes, Distance in graphs, 94b25, k-metric dimension, error-correcting code, grid graph, Combinatorics (math.CO), 05b40, Mathematics
05C12, 94B25, 05B40, 94B35, Decoding, Graph operations (line graphs, products, etc.), 94b35, k-resolving set, uncovering, error-correcting code, k-resolving set, covering design, QA1-939, FOS: Mathematics, Mathematics - Combinatorics, 05c12, uncovering, grid graph, Combinatorial aspects of packing and covering, \(k\)-resolving set, \(k\)-metric dimension, Combinatorial codes, Distance in graphs, 94b25, k-metric dimension, error-correcting code, grid graph, Combinatorics (math.CO), 05b40, Mathematics
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