Quantum Block and Convolutional Codes from Self-orthogonal Product Codes
<|reference_start|>Quantum Block and Convolutional Codes from Self-orthogonal Product Codes: 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.<|reference_end|>
@article{grassl2007quantum,
    title={Quantum Block and Convolutional Codes from Self-orthogonal Product Codes},
    author={Markus Grassl, Martin Roetteler},
    journal={Proceedings 2005 IEEE International Symposium on Information
  Theory (ISIT 2005), Adelaide, Australia, September 2005, pp. 1018-1022},
    year={2007},
    doi={10.1109/ISIT.2005.1523493},
    archivePrefix={arXiv},
    eprint={quant-ph/0703181},
    primaryClass={quant-ph cs.IT math.IT}
}