Quantum weight enumerators
- 1 July 1998
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 44 (4), 1388-1394
- https://doi.org/10.1109/18.681316
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 2Keywords
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This publication has 7 references indexed in Scilit:
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