Calderbank, A. Robert and Rains, Eric M. and Shor, P. W. and Sloane, Neil J. A. (1998) Quantum error correction via codes over GF(4). IEEE Transactions on Information Theory, 44 (4). pp. 1369-1387. ISSN 0018-9448. doi:10.1109/18.681315. https://resolver.caltech.edu/CaltechAUTHORS:20170925-160358492
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Abstract
The problem of finding quantum error correcting codes is transformed into the problem of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product. Many new codes and new bounds are presented, as well as a table of upper and lower bounds on such codes of length up to 30 qubits.
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| Additional Information: | © 1998 IEEE. Manuscript received July 15, 1996; revised December 4, 1997. The work of E. M. Rains was performed while he was with the Institute for Defense Analyses, Princeton, NJ USA. The material in this paper was presented in part at the IEEE International Symposium on Information Theory, Ulm, Germany, 1997. The authors wish to thank Aaron Gulliver for finding the quasicyclic codes mentioned in Section V, and our colleague Ronald H. Hardin for his contributions to our search for interesting nonadditive codes. We also thank Patrick Solé for drawing our attention to the work of B. Runge and G. Höhn. | ||||||||||||
| Subject Keywords: | Codes, additive; codes, quantum; codes, quaternary; codes, self-orthogonal, geometry, orthogonal; geometry, symplectic; group, Clifford | ||||||||||||
| Issue or Number: | 4 | ||||||||||||
| DOI: | 10.1109/18.681315 | ||||||||||||
| Record Number: | CaltechAUTHORS:20170925-160358492 | ||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170925-160358492 | ||||||||||||
| Official Citation: | A. R. Calderbank, E. M. Rains, P. M. Shor and N. J. A. Sloane, "Quantum error correction via codes over GF(4)," in IEEE Transactions on Information Theory, vol. 44, no. 4, pp. 1369-1387, Jul 1998. doi: 10.1109/18.681315 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=681315&isnumber=14976 | ||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
| ID Code: | 81821 | ||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||
| Deposited By: | Tony Diaz | ||||||||||||
| Deposited On: | 25 Sep 2017 23:12 | ||||||||||||
| Last Modified: | 15 Nov 2021 19:46 |
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