Nonbinary Quantum Goppa Codes Exceeding the Quantum Gilbert-Varshamov Bound

@article{Niehage2007NonbinaryQG,
  title={Nonbinary Quantum Goppa Codes Exceeding the Quantum Gilbert-Varshamov Bound},
  author={Annika Niehage},
  journal={Quantum Information Processing},
  year={2007},
  volume={6},
  pages={143-158}
}
An explicit construction for nonbinary quantum Goppa codes (often also called quantum AG codes) exceeding the quantum Gilbert-Varshamov bound is given. First a weighted symplectic inner product is introduced and a method how to transform weighted codes into quantum codes with respect to the standard symplectic inner product is given. Then families of quantum Goppa codes using a tower of function fields by Stichtenoth are constructed. Finally a proof that these codes lie above the quantum… CONTINUE READING

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Showing 1-10 of 11 references

Transitive and self-dual codes attaining the Tsfasman-Vladut-Zink bound", publication in preparation

  • H. STICHTENOTH
  • ANNIKA NIEHAGE, Universität Mannheim, Fakultät…
  • 2005
Highly Influential
3 Excerpts

WALKER - "Nonbinary quantum error-correcting codes from algebraic curves", submitted for publication

  • KIM J. J .-L
  • 2004
1 Excerpt

RÖTTELER - "Efficient quantum circuits for non-qubit quantum error-correcting codes

  • M. GRASSL, M. T. BETH
  • International Journal of Foundation of Computer…
  • 2003
1 Excerpt

KNILL - "Nonbinary quantum stabilizer codes

  • E. A. ASHIKHMIN
  • Transactions on Information Theory
  • 2001
1 Excerpt

TSFASMAN - "Asymptotically good quantum codes

  • A. ASHIKHMIN, M.A.S. LITSYN
  • Phys. Rev. A
  • 2001
1 Excerpt

XING - "Asymptotically good quantum codes exceeding the Ashikhmin-Litsyn- Tsfasman bound

  • H. CHEN, C. S. LING
  • IEEE Transactions on Information Theory
  • 2001
1 Excerpt

RAINS - "Nonbinary quantum codes

  • E M.
  • IEEE Transactions on Information Theory
  • 1999
1 Excerpt

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