Graph-based code[1,2] 

Description

Binary linear code whose generator matrix is defined using the adjacency matrix of a graph.

Given an adjacency matrix \(A\), the generator matrix is either \(G=A\) or \(G=(I|A)\), where \(I\) is the identity matrix.

Codes based on strongly regular graphs are sometimes optimal or nearly optimal for their length and size [1].

Parent

Cousin

References

[1]
V. D. Tonchev, “Binary codes derived from the Hoffman-Singleton and Higman-Sims graphs”, IEEE Transactions on Information Theory 43, 1021 (1997) DOI
[2]
V. D. Tonchev, “Error-correcting codes from graphs”, Discrete Mathematics 257, 549 (2002) DOI
Page edit log

Your contribution is welcome!

on github.com (edit & pull request)— see instructions

edit on this site

Zoo Code ID: graph

Cite as:
“Graph-based code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/graph
BibTeX:
@incollection{eczoo_graph, title={Graph-based code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/graph} }
Share via:
Twitter | Mastodon |  | E-mail
Permanent link:
https://errorcorrectionzoo.org/c/graph

Cite as:

“Graph-based code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/graph

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/bits/graph.yml.