\([[10,1,4]]_{G}\) tenfold code[1; Prop. V.1]
Description
A \([[10,1,4]]_{G}\) group code for finite Abelian \(G\). The code is defined using a graph that is closely related to the \([[5,1,3]]\) code.Cousins
- \([[5,1,3]]_{\mathbb{Z}_q}\) modular-qudit code— The \([[10,1,4]]_{G}\) Abelian group code for \(G=\mathbb{Z}_q\) is defined using a graph that is closely related to the \([[5,1,3]]_{\mathbb{Z}_q}\) modular-qudit code [1].
- \([[5,1,3]]_q\) Galois-qudit code— The \([[10,1,4]]_{G}\) Abelian group code for \(G=\mathbb{F}_q\) is defined using a graph that is closely related to the \([[5,1,3]]_{q}\) Galois-qudit code [1].
- \([[5,1,3]]\) Five-qubit perfect code— The \([[10,1,4]]_{G}\) Abelian group code for \(G=\mathbb{Z}_2\) is defined using a graph that is closely related to the \([[5,1,3]]\) five-qubit code [1]. The former code can be obtained by converting the latter into a code that is oblivious to collective \(Z\)-type rotations [2; Exam. 6].
Primary Hierarchy
Parents
The \([[10,1,4]]_{G}\) group code is defined using a graph [1; Prop. V.1].
\([[10,1,4]]_{G}\) tenfold code
References
- [1]
- D. Schlingemann and R. F. Werner, “Quantum error-correcting codes associated with graphs”, Physical Review A 65, (2001) arXiv:quant-ph/0012111 DOI
- [2]
- J. Hu, Q. Liang, N. Rengaswamy, and R. Calderbank, “Mitigating Coherent Noise by Balancing Weight-2 Z-Stabilizers”, IEEE Transactions on Information Theory 68, 1795 (2022) arXiv:2011.00197 DOI
Page edit log
- Victor V. Albert (2026-06-08) — most recent
- Victor V. Albert (2024-02-24)
Cite as:
“\([[10,1,4]]_{G}\) tenfold code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/group_10_1_4, arXiv:2606.11484