×

Error-correcting codes from graphs. (English) Zbl 1015.05041

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.

MSC:

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
94B05 Linear codes (general theory)
05C90 Applications of graph theory
PDFBibTeX XMLCite
Full Text: DOI