Error-correcting codes from graphs

Authors

Vladimir Tonchev, Michigan Technological UniversityFollow

Document Type

Article

Publication Date

11-2002

Abstract

The paper surveys some constructions of linear binary codes defined by the adjacency matrices of undirected graphs. It is shown that the class of all graphs with n vertices leads to codes that for large n meet the Gilbert–Varshamov bound. Some interesting codes are obtainable from graphs with high degree of symmetry, such as strongly regular graphs. A relation between the linear binary codes derived from graphs and a class of quantum error-correcting codes is also discussed.

Publisher's Statement

Copyright © 2002 Elsevier Science B.V. All rights reserved. Publisher’s version of record: https://doi.org/10.1016/S0012-365X(02)00513-7

Publication Title

Discrete Mathematics

Recommended Citation

Tonchev, V. (2002). Error-correcting codes from graphs. Discrete Mathematics, 257(2-3), 549-557. http://doi.org/10.1016/S0012-365X(02)00513-7
Retrieved from: https://digitalcommons.mtu.edu/math-fp/129