Tonchev, Vladimir D. Error-correcting codes from graphs. (English) Zbl 1015.05041 Discrete Math. 257, No. 2-3, 549-557 (2002). This paper considers linear codes constructed by using the row space of the matrix of an undirected graph, both with the identity matrix row space, and without it. It shows they include codes that attain the Gilbert-Varshamov bound, codes rapidly decodable by majority decoding, and codes usable for quantum-error-correction. Reviewer: Ki Hang Kim (Montgomery) Cited in 13 Documents MSC: 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.) 94B05 Linear codes (general theory) 05C90 Applications of graph theory Keywords:linear binary code; quantum-error-correcting code; Gilbert-Varshamov bound; majority decoding PDFBibTeX XMLCite \textit{V. D. Tonchev}, Discrete Math. 257, No. 2--3, 549--557 (2002; Zbl 1015.05041) Full Text: DOI