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2010

Quantum Cyclic Code

Dutta, Sagarmoy, Kurur, Piyush P

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In this paper, we define and study \emph{quantum cyclic codes}, a generalisation of cyclic codes to the quantum setting.

Previously studied examples of quantum cyclic codes were all quantum codes obtained from classical cyclic codes via the CSS construction.
However, the codes that we study are much more general.
In particular, we construct cyclic stabiliser codes with parameters $[[5,1,3]]$, $[[17,1,7]]$ and $[[17,9,3]]$, all of which are \emph{not} CSS.

Quantum Cyclic Code · Around

Built on

Good quantum error-correcting codes exist
A. R. Calderbank and P. W. Shor · 1996
Earlier work this paper cites.
A class of quantum error-correcting codes saturating the quantum hamming bound
D. Gottesman · 1996
Earlier work this paper cites.
Multiple particle interference and quantum error correction
A. M. Steane · 1996
Earlier work this paper cites.
Quantum error correction and orthogonal geometry
A. R. Calderbank, E. M. Rains, P. W. Shor, and N. J. A. Sloane · 1997
Earlier work this paper cites.
A nonadditive quantum code
E. M. Rains, R. H. Hardin, P. W. Shore, and A. S. N.J · 1997
Earlier work this paper cites.

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Then

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