\([[10,1,3;1,3,4]]\) EAOA Hamming code[1]
Description
An EAOA qubit stabilizer code constructed from the dual of a \([10,6,3]\) code obtained by shortening the classical \([15,11,3]\) Hamming code at five positions. In the notation of the parent entry, the example of Ref. [1] is a \([[10,1,3;1,3,4]]\) code: it encodes one logical qubit and four classical strings (equivalently, two classical bits), while retaining one gauge qubit and using three ebits.Cousins
- \([2^r-1,2^r-r-1,3]\) Hamming code— The dual of a \([10,6,3]\) code obtained by shortening the \([15,11,3]\) Hamming code at five positions can be used to construct \([[10,1,3;1,3,4]]\) EAOA Hamming code [1].
- Small-distance qubit stabilizer code
Member of code lists
Primary Hierarchy
Parents
\([[10,1,3;1,3,4]]\) EAOA Hamming code
References
- [1]
- P. J. Nadkarni, S. Adonsou, G. Dauphinais, D. W. Kribs, and M. Vasmer, “Unified and Generalized Approach to Entanglement-Assisted Quantum Error Correction”, (2024) arXiv:2411.14389
Page edit log
- Victor V. Albert (2026-03-27) — most recent
Cite as:
“\([[10,1,3;1,3,4]]\) EAOA Hamming code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/eaoa_hamming