Rains, Eric M. (1998) Quantum weight enumerators. IEEE Transactions on Information Theory, 44 (4). pp. 1388-1394. ISSN 0018-9448. doi:10.1109/18.681316. https://resolver.caltech.edu/CaltechAUTHORS:20170925-154039545
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Abstract
In a recent paper, Shor and Laflamme (see Phys. Rev. Lett., vol.78, p.1600-2, 1997) defined two "weight enumerators" for quantum error-correcting codes, connected by a MacWilliams transform, and used them to give a linear programming bound for quantum codes. We introduce two new enumerators which, while much less powerful at producing bounds, are useful tools nonetheless. The new enumerators are connected by a much simpler duality transform, clarifying the duality between Shor and Laflamme's enumerators. We also use the new enumerators to give a simpler condition for a quantum code to have specified minimum distance, and to extend the enumerator theory to codes with block size greater than 2.
Item Type: | Article | ||||||||||||
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Additional Information: | © 1998 IEEE. Manuscript received December 20, 1996; revised December 31, 1997. The author wishes to thank P. Shor and N. Sloane for many helpful discussions; he would also like to thank C. Bennett for a helpful discussion on erasures. | ||||||||||||
Subject Keywords: | Weight enumerators q-ary quantum codes | ||||||||||||
Issue or Number: | 4 | ||||||||||||
DOI: | 10.1109/18.681316 | ||||||||||||
Record Number: | CaltechAUTHORS:20170925-154039545 | ||||||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170925-154039545 | ||||||||||||
Official Citation: | E. M. Rains, "Quantum weight enumerators," in IEEE Transactions on Information Theory, vol. 44, no. 4, pp. 1388-1394, Jul 1998. doi: 10.1109/18.681316 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=681316&isnumber=14976 | ||||||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
ID Code: | 81818 | ||||||||||||
Collection: | CaltechAUTHORS | ||||||||||||
Deposited By: | Tony Diaz | ||||||||||||
Deposited On: | 25 Sep 2017 22:44 | ||||||||||||
Last Modified: | 15 Nov 2021 19:46 |
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