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Quantum Block and Convolutional Codes from Self-orthogonal Product Codes

Markus Grassl·Martin Roetteler
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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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Markus Grassl, Martin Roetteler. 2007-03-19. Quantum Block and Convolutional Codes from Self-orthogonal Product Codes. https://doi.org/10.1109/isit.2005.1523493

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