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)
Error-correcting pairs were introduced as a general method of decoding linear codes with respect to ...
[Abstract] An ordered set S of vertices of a graph G is a resolving set for G if every vertex is uni...
The paper surveys some constructions of linear binary codes defined by the adjacency matrices of und...
We demonstrate a construction of error-correcting codes from graphs by means of k-resolving sets, an...
A study of the efficiency, error-correcting capabilities, and limitations of graph theoretic block c...
AbstractWe replace the usual setting for error-correcting codes (i.e. vector spaces over finite fiel...
Error-correcting codes seek to address the problem of transmitting information efficiently and relia...
101 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2000.We consider two graph-based t...
In this paper we investigate correcting properties of LDPC codes obtained from families of algebraic...
An area of research in graph theory, in which a distance-based parameter, called a resolving set, is...
In this paper, we consider fault-tolerant resolving sets in graphs. We characterize n-vertex graphs ...
We develop an approach through geometric functional analysis to error correcting codes and ...
An l-resolving set of a graph G is a set of vertices that has a unique array of distances to all ver...
International audienceWe consider the problems of finding optimal identifying codes, (open) locating...
AbstractA perfect one-error-correcting code on a graph is a subset of the vertices so that no two ve...
Error-correcting pairs were introduced as a general method of decoding linear codes with respect to ...
[Abstract] An ordered set S of vertices of a graph G is a resolving set for G if every vertex is uni...
The paper surveys some constructions of linear binary codes defined by the adjacency matrices of und...
We demonstrate a construction of error-correcting codes from graphs by means of k-resolving sets, an...
A study of the efficiency, error-correcting capabilities, and limitations of graph theoretic block c...
AbstractWe replace the usual setting for error-correcting codes (i.e. vector spaces over finite fiel...
Error-correcting codes seek to address the problem of transmitting information efficiently and relia...
101 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2000.We consider two graph-based t...
In this paper we investigate correcting properties of LDPC codes obtained from families of algebraic...
An area of research in graph theory, in which a distance-based parameter, called a resolving set, is...
In this paper, we consider fault-tolerant resolving sets in graphs. We characterize n-vertex graphs ...
We develop an approach through geometric functional analysis to error correcting codes and ...
An l-resolving set of a graph G is a set of vertices that has a unique array of distances to all ver...
International audienceWe consider the problems of finding optimal identifying codes, (open) locating...
AbstractA perfect one-error-correcting code on a graph is a subset of the vertices so that no two ve...
Error-correcting pairs were introduced as a general method of decoding linear codes with respect to ...
[Abstract] An ordered set S of vertices of a graph G is a resolving set for G if every vertex is uni...
The paper surveys some constructions of linear binary codes defined by the adjacency matrices of und...
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