Petersen cycle code[1] 

Description

A \([15,6,5]\) cycle code whose parity-check matrix is the incidence matrix of the Petersen graph. The Petersen graph can be thought of as a dodecahedron with antipodes identified [2; Appx. A.2.1].

Notes

See more details, see [3; Example 10.11.7].

Parents

References

[1]
S. Hakimi and J. Bredeson, “Graph theoretic error-correcting codes”, IEEE Transactions on Information Theory 14, 584 (1968) DOI
[2]
J. Haah et al., “Magic state distillation with low space overhead and optimal asymptotic input count”, Quantum 1, 31 (2017) arXiv:1703.07847 DOI
[3]
D. Jungnickel, Graphs, Networks and Algorithms (Springer Berlin Heidelberg, 2008) DOI
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Zoo Code ID: petersen

Cite as:
“Petersen cycle code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/petersen
BibTeX:
@incollection{eczoo_petersen, title={Petersen cycle code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/petersen} }
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Cite as:

“Petersen cycle code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/petersen

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