dorsal/arxiv
View SchemaQuantum Block and Convolutional Codes from Self-orthogonal Product Codes
| Authors | Markus Grassl, Martin Roetteler |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0703181 |
| URL | https://arxiv.org/abs/quant-ph/0703181 |
| DOI | 10.1109/ISIT.2005.1523493 |
| Journal | Proceedings 2005 IEEE International Symposium on Information Theory (ISIT 2005), Adelaide, Australia, September 2005, pp. 1018-1022 |
Abstract
We present a construction of self-orthogonal codes using product codes. From the resulting codes, one can construct both block quantum error-correcting codes and quantum convolutional codes. We show that from the examples of convolutional codes found, we can derive ordinary quantum error-correcting codes using tail-biting with parameters [[42N,24N,3]]_2. While it is known that the product construction cannot improve the rate in the classical case, we show that this can happen for quantum codes: we show that a code [[15,7,3]]_2 is obtained by the product of a code [[5,1,3]]_2 with a suitable code.
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"abstract": "We present a construction of self-orthogonal codes using product codes. From\nthe resulting codes, one can construct both block quantum error-correcting\ncodes and quantum convolutional codes. We show that from the examples of\nconvolutional codes found, we can derive ordinary quantum error-correcting\ncodes using tail-biting with parameters [[42N,24N,3]]_2. While it is known that\nthe product construction cannot improve the rate in the classical case, we show\nthat this can happen for quantum codes: we show that a code [[15,7,3]]_2 is\nobtained by the product of a code [[5,1,3]]_2 with a suitable code.",
"arxiv_id": "quant-ph/0703181",
"authors": [
"Markus Grassl",
"Martin Roetteler"
],
"categories": [
"quant-ph",
"cs.IT",
"math.IT"
],
"doi": "10.1109/ISIT.2005.1523493",
"journal_ref": "Proceedings 2005 IEEE International Symposium on Information\n Theory (ISIT 2005), Adelaide, Australia, September 2005, pp. 1018-1022",
"title": "Quantum Block and Convolutional Codes from Self-orthogonal Product Codes",
"url": "https://arxiv.org/abs/quant-ph/0703181"
},
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