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Quantum block and convolutional codes from self-orthogonal product codes

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2 Author(s)
Grassl, M. ; Institut fur Algorithmen und Kognitive Syst., Karlsruhe Univ. ; Rotteler, M.

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

Published in:

Information Theory, 2005. ISIT 2005. Proceedings. International Symposium on

Date of Conference:

4-9 Sept. 2005