Petersen cycle code

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

Member of code lists

Primary Hierarchy

Classical Domain

Galois-field Kingdom

\(q\)-ary codeECC

Additive \(q\)-ary codeECC

Linear \(q\)-ary codeECC

Projective geometry code

Cycle code

Parents

Cycle code

Small-distance block codeECC

Petersen cycle code

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

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