SCIENCE CHINA Information Sciences, Volume 63 , Issue 4 : 149301(2020) https://doi.org/10.1007/s11432-019-9871-y

## On the parity-check matrix of generalized concatenated code

• AcceptedApr 18, 2019
• PublishedSep 12, 2019
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### Acknowledgment

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.

### Supplement

Appendixes A and B.

### References

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

[2] Dumer I. Concatenated codes and their multilevel generatlizations. In: Handbook of coding Theory. Amsterdam: Elsevier, 1998. 1911--1988. Google Scholar

[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 Theor, 2016, 62: 5343-5358 CrossRef Google Scholar

[4] Gao J, Wang X F, Shi M J. Gray maps on linear codes over $\mathbb{F}_p[v]/(v^m-v)$ and their applications. Sci Sin Math, 2016, 46: 1329-1336 CrossRef Google Scholar

[5] Maucher J, Zyablov V V, Bossert M. On the equivalence of generalized concatenated codes and generalized error location codes. IEEE Trans Inform Theor, 2000, 46: 642-649 CrossRef Google Scholar

[6] Wardlaw W P. Matrix Representation of Finite Fields. Math Mag, 1994, 67: 289-293 CrossRef Google Scholar

[7] Poulin D. Optimal and efficient decoding of concatenated quantum block codes. Phys Rev A, 2006, 74: 052333 CrossRef ADS Google Scholar

[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. Google Scholar

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