5 Stabilizer Codes
Another goal of this project was to investigate an important subclass of Clifford codes, namely stabilizer codes over nonbinary fields. In the publications given below, we develop the theory of such codes, derive many new code constructions, find bounds, and construct many new code families.
- P. Sarvepalli
and A. Klappenecker. Nonbinary quantum Reed-Muller codes.
In Proc. 2005 IEEE International Symposium on Information Theory,
Adelaide, Australia, pages 1023–1027, 2005
@InProceedings{klappenecker050,
author = {Sarvepalli, P. and Klappenecker, A.},
title = {Nonbinary Quantum {R}eed-{M}uller Codes},
booktitle = {Proc. 2005 IEEE International Symposium on Information Theory,
Adelaide, Australia},
pages = {1023-1027},
year = 2005
}
- P.K. Sarvepalli and A. Klappenecker. Nonbinary quantum codes from
hermitian curves. In M. et al. Fossorier, editor, Applied Algebra, Algebraic
Algorithms and Error-Correcting Codes: 16th International Symposium,
AAECC-16, Las Vegas, NV, USA, February 20-24, 2006. Proceedings, volume
3857 of LNCS, pages 136–143. Springer-Verlag, 2006
@InProceedings{klappenecker055,
author = {Sarvepalli, P.K. and Klappenecker, A.},
title = {Nonbinary quantum codes from Hermitian curves},
booktitle = {Applied Algebra, Algebraic Algorithms and Error-Correcting
Codes: 16th International Symposium, AAECC-16,
Las Vegas, NV, USA, February 20-24, 2006. Proceedings},
year = 2006,
editor = {Fossorier, M. et al.},
volume = 3857,
series = {LNCS},
publisher = {Springer-Verlag},
pages = {136-143}
} - S.A. Aly, A. Klappenecker, and P.K. Sarvepalli. Primitive quantum BCH codes
over finite fields. In Proc. 2006 IEEE International Symposium on Information
Theory, Seattle, USA, pages 1105–1108, 2006
@InProceedings{klappenecker058,
author = {Aly, S.A. and Klappenecker, A. and Sarvepalli, P.K.},
title = {Primitive Quantum {BCH} Codes over Finite Fields},
booktitle = {Proc. 2006 IEEE International Symposium on Information Theory, Seattle, USA},
pages = {1105-1108},
year = 2006
} - S.A. Aly, A. Klappenecker, and P.K. Sarvepalli. Remarkable degenerate
quantum stabilizer codes derived from duadic codes. In Proc. 2006 IEEE
International Symposium on Information Theory, Seattle, USA, pages
1114–1118, 2006
@InProceedings{klappenecker059,
author = {Aly, S.A. and Klappenecker, A. and Sarvepalli, P.K.},
title = {Remarkable Degenerate Quantum Stabilizer Codes Derived from Duadic Codes},
booktitle = {Proc. 2006 IEEE International Symposium on Information Theory, Seattle, USA},
pages = {1114-1118},
year = 2006
} - A. Ketkar, A. Klappenecker, S. Kumar, and P.K. Sarvepalli. Nonbinary stabilizer
codes over finite fields. IEEE Trans. Inform. Theory, 52(11):4892–4914,
2006
@Article{klappenecker060,
author = {Ketkar, A. and Klappenecker, A. and Kumar, S. and Sarvepalli, P.K. },
title = {Nonbinary Stabilizer Codes over Finite Fields },
journal = {IEEE Trans. Inform. Theory},
year = 2006,
volume = 52,
number = 11,
pages = {4892-4914}
} - S.A. Aly, A. Klappenecker, and P.K. Sarvepalli. On quantum and
classical BCH codes. IEEE Trans. Inform. Theory, 53(3):1183–1188,
2007
@Article{klappenecker064,
author = {Aly, S.A. and Klappenecker, A. and Sarvepalli, P.K.},
title = {On quantum and classical {BCH} codes},
journal = {IEEE Trans. Inform. Theory},
year = 2007,
volume = 53,
number = 3,
pages = {1183-1188}
} - P.K. Sarvepalli, S.A. Aly, and A. Klappenecker. Nonbinary stabilizer
codes. In G. Chen, L. Kauffman, and S. Lomonaco, editors, The
Mathematics of Quantum Computation and Quantum Technology.
2007
@InCollection{klappenecker065,
author = {Sarvepalli, P.K. and S.A. Aly and Klappenecker, A.},
title = {Nonbinary stabilizer codes},
booktitle = {The Mathematics of Quantum Computation and Quantum Technology},
publisher = {Taylor \& Francis},
year = 2007,
editor = {Chen, G. and Kauffman, L. and Lomonaco, S.}
}