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

Description

A graph-based code whose generator matrix is constructed using the adjacency matrix \(A\) of the Hoffman-Sims graph. Setting the generator matrix \(G=(I|A)\) yields a \([100,22,32]\) code whose dual is an optimal \([100,78,8]\) code [1; Table VI].

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
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Zoo Code ID: hoffman-sims_graph

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

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

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