dorsal/arxiv
View SchemaQuantum Weight Enumerators
| Authors | Eric M. Rains |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9612015 |
| URL | https://arxiv.org/abs/quant-ph/9612015 |
Abstract
In a recent paper ([quant-ph/9610040]), Shor and Laflamme define two ``weight enumerators'' for quantum error correcting codes, connected by a MacWilliams transform, and use 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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"abstract": "In a recent paper ([quant-ph/9610040]), Shor and Laflamme define two ``weight\nenumerators\u0027\u0027 for quantum error correcting codes, connected by a MacWilliams\ntransform, and use them to give a linear-programming bound for quantum codes.\nWe introduce two new enumerators which, while much less powerful at producing\nbounds, are useful tools nonetheless. The new enumerators are connected by a\nmuch simpler duality transform, clarifying the duality between Shor and\nLaflamme\u0027s enumerators. We also use the new enumerators to give a simpler\ncondition for a quantum code to have specified minimum distance, and to extend\nthe enumerator theory to codes with block-size greater than 2.",
"arxiv_id": "quant-ph/9612015",
"authors": [
"Eric M. Rains"
],
"categories": [
"quant-ph"
],
"title": "Quantum Weight Enumerators",
"url": "https://arxiv.org/abs/quant-ph/9612015"
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