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On the parity-check matrix of generalized concatenated code

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References

  1. 1

    Lin S, Costello D J. Error Control Coding. 2nd ed. Upper Saddle River: Prentice-Hall, 2004

  2. 2

    Dumer I. Concatenated codes and their multilevel generatlizations. In: Handbook of Coding Theory. Amsterdam: Elsevier, 1998. 1911–1988

  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: 5343–5358

  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: 1329–1336

  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: 642–649

  6. 6

    Wardlaw W P. Matrix representation of finite fields. Math Mag, 1994, 67: 289–293

  7. 7

    Poulin D. Optimal and efficient decoding of concatenated quantum block codes. Phys Rev A, 2006, 74: 052333

  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. 529–533

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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.

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Correspondence to Yang Liu or Yunjiang Wang.

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Shi, S., Liu, Y., Yan, J. et al. On the parity-check matrix of generalized concatenated code. Sci. China Inf. Sci. 63, 149301 (2020). https://doi.org/10.1007/s11432-019-9871-y

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