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].Cousins
- Dodecahedron code— The Petersen graph can be thought of as a dodecahedron with antipodes identified [2; Appx. A.2.1].
- Petersen spherical code
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References
- [1]
- S. Hakimi and J. Bredeson, “Graph theoretic error-correcting codes”, IEEE Transactions on Information Theory 14, 584 (1968) DOI
- [2]
- J. Haah, M. B. Hastings, D. Poulin, and D. Wecker, “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
Page edit log
- Victor V. Albert (2024-03-16) — most recent
Cite as:
“Petersen cycle code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/petersen