Advertisement

On the parity-check matrix of generalized concatenated code

  • Sha Shi
  • Yang LiuEmail author
  • Junzhi Yan
  • Jingliang Gao
  • Yunjiang WangEmail author
Letter

Notes

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61771377, 61502376, 61703175), Projects of International Cooperation and Exchanges of Shannxi Province (Grant Nos. 2017KW-003, 2016KW-037), and Fundamental Research Funds for the Central Universities.

Supplementary material

11432_2019_9871_MOESM1_ESM.pdf (231 kb)
On the parity-check matrix of generalized concatenated code

References

  1. 1.
    Lin S, Costello D J. Error Control Coding. 2nd ed. Upper Saddle River: Prentice-Hall, 2004zbMATHGoogle Scholar
  2. 2.
    Dumer I. Concatenated codes and their multilevel generatlizations. In: Handbook of Coding Theory. Amsterdam: Elsevier, 1998. 1911–1988Google Scholar
  3. 3.
    Lin S J, Al-Naffouri T Y, Han Y S. FFT algorithm for binary extension finite fields and its application to reed-solomon codes. IEEE Trans Inform Theory, 2016, 62: 5343–5358MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Gao J, Wang X F, Shi M J, et al. Gray maps on linear codes over \({\mathbb{F}_p}[v]/({v^m} - v)\) and their applications. Sci Sin Math, 2016, 46: 1329–1336Google Scholar
  5. 5.
    Maucher J, Zyablov V V, Bossert M. On the equivalence of generalized concatenated codes and generalized error location codes. IEEE Trans Inform Theory, 2000, 46: 642–649MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Wardlaw W P. Matrix representation of finite fields. Math Mag, 1994, 67: 289–293MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Poulin D. Optimal and efficient decoding of concatenated quantum block codes. Phys Rev A, 2006, 74: 052333CrossRefGoogle Scholar
  8. 8.
    Wang Y J, Zeng B, Grassl M, et al. Stabilzier formalism for generalized concatenated quantum codes. In: Proceedings of IEEE International Symposium on Information Theory, Istanbul, 2013. 529–533Google Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Engineering Research Center of Molecular and Neuro Imaging Ministry of Education, School of Life Science and TechnologyXidian UniversityXi’anChina
  2. 2.National Computer Network Emergency Response Technical Team/Coordination Center of ChinaBeijingChina
  3. 3.China Mobile Research InstituteBeijingChina
  4. 4.State Key Laboratory of Integrated Services NetworksXidian UniversityXi’anChina

Personalised recommendations