Subsystem Codes
<|reference_start|>Subsystem Codes: We investigate various aspects of operator quantum error-correcting codes or, as we prefer to call them, subsystem codes. We give various methods to derive subsystem codes from classical codes. We give a proof for the existence of subsystem codes using a counting argument similar to the quantum Gilbert-Varshamov bound. We derive linear programming bounds and other upper bounds. We answer the question whether or not there exist [[n,n-2d+2,r>0,d]]<sub>q</sub> subsystem codes. Finally, we compare stabilizer and subsystem codes with respect to the required number of syndrome qudits.<|reference_end|>
@article{aly2006subsystem,
    title={Subsystem Codes},
    author={Salah A. Aly, Andreas Klappenecker, Pradeep Kiran Sarvepalli},
    journal={arXiv preprint arXiv:quant-ph/0610153},
    year={2006},
    archivePrefix={arXiv},
    eprint={quant-ph/0610153},
    primaryClass={quant-ph cs.IT math.IT}
}