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Quantum weight enumerators

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.

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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.

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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
Record Number:CaltechAUTHORS:20170925-154039545
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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:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81818
Deposited By: Tony Diaz
Deposited On:25 Sep 2017 22:44
Last Modified:15 Nov 2021 19:46

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