dorsal/arxiv
View SchemaOn Quantum and Classical BCH Codes
| Authors | Salah A. Aly, Andreas Klappenecker, Pradeep Kiran Sarvepalli |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0604102 |
| URL | https://arxiv.org/abs/quant-ph/0604102 |
Abstract
Classical BCH codes that contain their (Euclidean or Hermitian) dual codes can be used to construct quantum stabilizer codes; this correspondence studies the properties of such codes. It is shown that a BCH code of length n can contain its dual code only if its designed distance d=O(sqrt(n)), and the converse is proved in the case of narrow-sense codes. Furthermore, the dimension of narrow-sense BCH codes with small design distance is completely determined, and - consequently - the bounds on their minimum distance are improved. These results make it possible to determine the parameters of quantum BCH codes in terms of their design parameters.
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"abstract": "Classical BCH codes that contain their (Euclidean or Hermitian) dual codes\ncan be used to construct quantum stabilizer codes; this correspondence studies\nthe properties of such codes. It is shown that a BCH code of length n can\ncontain its dual code only if its designed distance d=O(sqrt(n)), and the\nconverse is proved in the case of narrow-sense codes. Furthermore, the\ndimension of narrow-sense BCH codes with small design distance is completely\ndetermined, and - consequently - the bounds on their minimum distance are\nimproved. These results make it possible to determine the parameters of quantum\nBCH codes in terms of their design parameters.",
"arxiv_id": "quant-ph/0604102",
"authors": [
"Salah A. Aly",
"Andreas Klappenecker",
"Pradeep Kiran Sarvepalli"
],
"categories": [
"quant-ph"
],
"title": "On Quantum and Classical BCH Codes",
"url": "https://arxiv.org/abs/quant-ph/0604102"
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