Hoffman-Singleton graph-adjacency code[1,2] 

Description

A graph-based code whose generator matrix is constructed using the adjacency matrix of the Hoffman-Singleton graph [3]. Setting the generator matrix equal to the adjacency matrix, \(G=A\), yields a \([50,22,7]\) code whose dual is a \([50,28,8]\) code [1; Table III].

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
[3]
A. J. Hoffman and R. R. Singleton, “On Moore Graphs with Diameters 2 and 3”, IBM Journal of Research and Development 4, 497 (1960) DOI
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Zoo Code ID: hoffman-singleton_graph

Cite as:
“Hoffman-Singleton graph-adjacency code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/hoffman-singleton_graph
BibTeX:
@incollection{eczoo_hoffman-singleton_graph, title={Hoffman-Singleton graph-adjacency code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/hoffman-singleton_graph} }
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Cite as:

“Hoffman-Singleton graph-adjacency code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/hoffman-singleton_graph

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