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A group theoretic framework is introduced that simplifies the description of known quantum error-correcting codes and greatly facilitates the construction of new examples. Codes are given which map 3 qubits to 8 qubits correcting 1 error, 4 to 10 qubits correcting 1 error, 1 to 13 qubits correcting 2 errors, and 1 to 29 qubits correcting 5 errors.
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A.R. Calderbank
Duke University
Eric M. Rains
California Institute of Technology
Peter W. Shor
AT&T (United States)
CERN Bulletin
Physical Review Letters
AT&T (United States)
Institute For Defense Analyses
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Calderbank et al. (Mon,) studied this question.
synapsesocial.com/papers/69d75afaf07a12db70b8ab68 — DOI: https://doi.org/10.1103/physrevlett.78.405