Quantum Block and Convolutional Codes from Self-orthogonal Product Codes

Details Quantum Block and Convolutional Codes from Self-orthogonal Product Codes Quantum Block and Convolutional Codes from Self-orthogonal Product Codes

2007-03-19

arxiv.org/abs/quant-ph/0703181v1

Proceedings 2005 IEEE International Symposium on Information Theory (ISIT 2005), Adelaide, Australia, September 2005, pp. 1018

Physics

Quantum Physics

5 pages, paper presented at the 2005 IEEE International Symposium on Information Theory

Scientific paper

10.1109/ISIT.2005.1523493

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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