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Journals / Mathematical Sciences and Applications E-Notes / 2019 / Cilt: 7 - Sayı: 1

The Quantum Codes over Fq and Quantum Quasi-cyclic Codes over Fp

Yasemin ÇENGELLENMİŞ
Abdullah DERTLİ
Pages
87–93
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Morever, the quantum quasi-cyclic codes over Fp are obtained, by using the self dual basis for Fps over Fp.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, the quantum codes over Fq are constructed by using the cyclic codes over the finite ring R = Fq + vFq + ... + v m−1Fq, where p is prime, q = p s , m − 1|p − 1 and v m = v.
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Key Findings & Data:The parameters of quantum error correcting codes over Fq are obtained.
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Conclusion & Impact:Morever, the quantum quasi-cyclic codes over Fp are obtained, by using the self dual basis for Fps over Fp.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Özet

In this paper, the quantum codes over Fq are constructed by using the cyclic codes over the finite ring R = Fq + vFq + ... + v m−1Fq, where p is prime, q = p s , m − 1|p − 1 and v m = v. The parameters of quantum error correcting codes over Fq are obtained. Some examples are given. Morever, the quantum quasi-cyclic codes over Fp are obtained, by using the self dual basis for Fps over Fp.

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Cite This Article

ÇENGELLENMİŞ, Y., DERTLİ, A. (2019). The Quantum Codes over Fq and Quantum Quasi-cyclic Codes over Fp. Mathematical Sciences and Applications E-Notes, Cilt: 7 - Sayı: 1, 87–93. https://ajindex.com/articles/283491

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References (18)

  1. Dertli, A., Cengellenmis, Y. and Eren, S., Quantum codes over F2 + uF2 + vF2. Palestine Journal of Math. (2015), 1-6
  2. Dertli, A., Cengellenmis, Y. and Eren, S., Some results on the linear codes over the finite ring F2+v1F2+.+vrF2. International Journal of Quantum Information 14(2016), 1650012
  3. Dertli, A., Cengellenmis, Y. and Eren, S., On quantum codes obtained from cyclic codes over A2. Int. J. Quantum Inform. 13 (2015), 1550031
  4. Dertli, A., Cengellenmis, Y. and Eren, S., Quantum codes over the ring F2 + uF2 + u 2F2 +. + u mF2. Int. Journal of Alg. 9(2015), 115 - 121
  5. Calderbank, A.R., Rains, E.M., Shor, P.M. and Sloane, N.J.A., Quantum error correction via codes over GF (4). IEEE Trans. Inf. Theory 44( 1998), 1369-1387
  6. Melakheso, A. and Guenda, K., The dual and the Gray image of codes over Fq +vFq +v 2Fq, arXiv:1504.08097v1
  7. Seroussi, G. and Lempel, A., Factorization of Symmetric Matrices and Trace-Orthogonal Bases in Finite Fields, SIAM. Journal Comput. 9(1980), 758-767
  8. Gao, J., Quantum codes from cyclic codes over Fq + vFq + v 2Fq + v 3Fq. Int. Journal of Quantum Information, 2015
  9. Qian, J., Quantum codes from cyclic codes over F2 + vF2. Journal of Inform.& computational Science 10( 2013), 1715-1722
  10. Qian, J., Ma, W. and Gou, W., Quantum codes from cyclic codes over finite ring. Int. J. Quantum Inform. 7( 2009), 1277-1283
  11. Qian, J., Ma, W. and X. Wang, Quantum error correcting codes from quasi-cyclic codes over finite ring. Int. J. Quantum Inform. 6( 2008), 1263-1269
  12. Shi, M. and Yao, T., Skew cyclic codes over Fq + vFq + v 2Fq +. + v m−1Fq, 2016
  13. Sari, M and Siap, I., On Quantum codes from cyclic codes over a class of non chain rings. Bull Korean Math. Soc. 53(2016), 617-1628
  14. Ashraf, M. and Mohammad, G., Quantum codes from cyclic codes over F3 + vF3. International Journal of Quantum Information 12(2014), 1450042
  15. Ashraf, M. and Mohammad, G., Construction of quantum codes from cyclic codes over Fp + vFp. International Journal of Information and Coding Theory 2(2015), 137-144
  16. Ashraf, M. and Mohammad, G., Quantum codes from cyclic codes over Fq + uFq + vFq + uvFq. Quantum Information Processing 10(2016), 4089-4098
  17. Kai, X. and Zhu, S., Quaternary construction of quantum codes from cyclic codes over F4 + uF4. Int. J. Quantum Inform. 9( 2011), 689-700
  18. Yin, X. and Ma, W., Gray Map and Quantum Codes Over The Ring F2+uF2+u 2F2. International Joint Conferences of IEEE