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Quantum shadow enumerators

Rains, Eric M. (1999) Quantum shadow enumerators. IEEE Transactions on Information Theory, 45 (7). pp. 2361-2366. ISSN 0018-9448. doi:10.1109/18.796376.

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In a previous paper, Shor and Laflamme (see Phys. Rev. Lett., vol.78, p.1600-02, 1997) define two "weight enumerators" for quantum error-correcting codes, connected by a MacWilliams (1977) transform, and use them to give a linear-programming bound for quantum codes. We extend their work by introducing another enumerator, based on the classical theory of shadow codes, that tightens their bounds significantly. In particular, nearly all of the codes known to be optimal among additive quantum codes (codes derived from orthogonal geometry) can be shown to be optimal among all quantum codes. We also use the shadow machinery to extend a bound on additive codes to general codes, obtaining as a consequence that any code of length, can correct at most [(n+1)/6] errors.

Item Type:Article
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Additional Information:© 1999 IEEE. Manuscript received November 20, 1996; revised January 12, 1999. The author wish to thank P. Shor and N. Sloane for many helpful discussions.
Subject Keywords:Linear programming, quantum error-correcting codes, shadow, upper bounds
Issue or Number:7
Record Number:CaltechAUTHORS:20170926-145724451
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Official Citation:E. M. Rains, "Quantum shadow enumerators," in IEEE Transactions on Information Theory, vol. 45, no. 7, pp. 2361-2366, Nov 1999. doi: 10.1109/18.796376 URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81850
Deposited By: Tony Diaz
Deposited On:26 Sep 2017 22:42
Last Modified:15 Nov 2021 19:46

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