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Quantum Codes

Year 2020, , 556 - 562, 01.03.2020

Abdullah Dertli , Yasemin Çengellenmiş

https://doi.org/10.21597/jist.569915

Abstract


In the present paper, the quantum
codes over Fq which are obtained from cyclic codes over the finite ring R=Fq+uFq +vFq+uvFq+v2Fq+uv2Fq with u2=1,v3=v ,uv=vu where q=pm and p is an odd prime. Moreover the parameters of quantum codes
over Fq are determined. Some examples are given.

Keywords

Qunatum codes Gray map cyclic codes

References

  • Ashraf M, Mohammad G, 2014. Quantum codes from cyclic codes over . International Journal of Quantum Information, 12 (6):1450042.
  • Ashraf M, Mohammad G, 2015. Construction of quantum codes from cyclic codes over . International Journal of Information and Coding Theory, 2 : 137-144. Ashraf M, Mohammad G, Quantum codes from cyclic codes over . Quantum Information Processing, DOI:10.1007/s11128-016-1379-8.
  • Calderbank A R, Rains E M, Shor P M, Sloane N J A, 1998. Quantum error correction via codes over GF(4). IEEE Transactions on Information Theory, 44:1369-1387.
  • Dertli A, Cengellenmis Y, Eren S, 2015a. On quantum codes obtained from cyclic codes over . International Journal of Quantum Information, 13: 1550031.
  • Dertli A, Cengellenmis Y, Eren S, 2015b. Quantum Codes over the Ring . International Journal of Algebra, 9: 115-121.
  • Dertli A, Cengellenmis Y, Eren S, 2016a. On the linear codes over the ring . Discrete Mathematics, Algorithms and Applications, 1650036.
  • Dertli A, Cengellenmis Y, Eren S, 2015c. On the Codes over a Semilocal Finite Ring. Intern. J. of Adv. Computer Science & Application, DOI: 10.14569/IJACSA.2015.061038.
  • Dertli A, Cengellenmis Y, Eren S, 2016b. Some results on the linear codes over the finite ring . International Journal of Quantum Information, 1650012.
  • Dertli A, Cengellenmis Y, Eren S, 2015d. Quantum Codes Over . Palestine Journal of Mathematics, 4: 547-552.
  • Kai X, Zhu S, 2011. Quaternary construction bof quantum codes from cyclic codes over . International Journal of Quantum Information, 9:689-700.
  • Liu Y, Shi M, Lu Z, 2017. Skew cyclic codes over . IEICE Transactions Fundamentals, DOI:101587/transfun.E0.A.1.
  • Qian J, 2013. Quantum codes from cyclic codes over . Journal of Information computational Science, 10:1715-1722.
  • Qian J, Ma W, Gou W, 2009. Quantum codes from cyclic codes over finite ring. International Journal of Quantum Information, 7:1277-1283.
  • Shor P W, 1995. Scheme for reducing decoherence in quantum memory. Phys. Rev. A, 52:2493-2496.
  • Steane A M, 1996. Simple quantum error correcting codes. Phys. Rev. A, 54:4741-4751.
  • Yin X, Ma W, 2011. Gray map and quantum codes over the ring . In Trust, Security and Privacy in Computing and Communications (TrustCom). IEEE 10th International Conference on, p:897-899.

Kuantum Kodlar

Year 2020, , 556 - 562, 01.03.2020

Abdullah Dertli , Yasemin Çengellenmiş

https://doi.org/10.21597/jist.569915

Abstract

Bu çalışmada,u2=1,v3=v ,uv=vu,q=pm   ve p tek asal sayı olmak üzere R=Fq+uFq +vFq+uvFq+v2Fq+uv2Fq    halkası üzerindeki devirli kodlar kullanılarak Fq üzerindeki kuantum kodlar elde edildi. Ayrıca, Fq üzerindeki kuantum kodların parametreleri belirlendi. Bazı örnekler verildi

Keywords

Kuantum kodlar devirli kodlar Gray dönüşümü

References

  • Ashraf M, Mohammad G, 2014. Quantum codes from cyclic codes over . International Journal of Quantum Information, 12 (6):1450042.
  • Ashraf M, Mohammad G, 2015. Construction of quantum codes from cyclic codes over . International Journal of Information and Coding Theory, 2 : 137-144. Ashraf M, Mohammad G, Quantum codes from cyclic codes over . Quantum Information Processing, DOI:10.1007/s11128-016-1379-8.
  • Calderbank A R, Rains E M, Shor P M, Sloane N J A, 1998. Quantum error correction via codes over GF(4). IEEE Transactions on Information Theory, 44:1369-1387.
  • Dertli A, Cengellenmis Y, Eren S, 2015a. On quantum codes obtained from cyclic codes over . International Journal of Quantum Information, 13: 1550031.
  • Dertli A, Cengellenmis Y, Eren S, 2015b. Quantum Codes over the Ring . International Journal of Algebra, 9: 115-121.
  • Dertli A, Cengellenmis Y, Eren S, 2016a. On the linear codes over the ring . Discrete Mathematics, Algorithms and Applications, 1650036.
  • Dertli A, Cengellenmis Y, Eren S, 2015c. On the Codes over a Semilocal Finite Ring. Intern. J. of Adv. Computer Science & Application, DOI: 10.14569/IJACSA.2015.061038.
  • Dertli A, Cengellenmis Y, Eren S, 2016b. Some results on the linear codes over the finite ring . International Journal of Quantum Information, 1650012.
  • Dertli A, Cengellenmis Y, Eren S, 2015d. Quantum Codes Over . Palestine Journal of Mathematics, 4: 547-552.
  • Kai X, Zhu S, 2011. Quaternary construction bof quantum codes from cyclic codes over . International Journal of Quantum Information, 9:689-700.
  • Liu Y, Shi M, Lu Z, 2017. Skew cyclic codes over . IEICE Transactions Fundamentals, DOI:101587/transfun.E0.A.1.
  • Qian J, 2013. Quantum codes from cyclic codes over . Journal of Information computational Science, 10:1715-1722.
  • Qian J, Ma W, Gou W, 2009. Quantum codes from cyclic codes over finite ring. International Journal of Quantum Information, 7:1277-1283.
  • Shor P W, 1995. Scheme for reducing decoherence in quantum memory. Phys. Rev. A, 52:2493-2496.
  • Steane A M, 1996. Simple quantum error correcting codes. Phys. Rev. A, 54:4741-4751.
  • Yin X, Ma W, 2011. Gray map and quantum codes over the ring . In Trust, Security and Privacy in Computing and Communications (TrustCom). IEEE 10th International Conference on, p:897-899.
There are 16 citations in total.

Details

Primary Language Turkish
Subjects Mathematical Sciences
Journal Section Matematik / Mathematics
Authors

Abdullah Dertli 0000-0001-8687-032X

Yasemin Çengellenmiş This is me 0000-0002-8133-9836

Publication Date March 1, 2020
Submission Date May 24, 2019
Acceptance Date October 8, 2019
Published in Issue Year 2020

Cite

APA Dertli, A., & Çengellenmiş, Y. (2020). Kuantum Kodlar. Journal of the Institute of Science and Technology, 10(1), 556-562. https://doi.org/10.21597/jist.569915
AMA Dertli A, Çengellenmiş Y. Kuantum Kodlar. J. Inst. Sci. and Tech. March 2020;10(1):556-562. doi:10.21597/jist.569915
Chicago Dertli, Abdullah, and Yasemin Çengellenmiş. “Kuantum Kodlar”. Journal of the Institute of Science and Technology 10, no. 1 (March 2020): 556-62. https://doi.org/10.21597/jist.569915.
EndNote Dertli A, Çengellenmiş Y (March 1, 2020) Kuantum Kodlar. Journal of the Institute of Science and Technology 10 1 556–562.
IEEE A. Dertli and Y. Çengellenmiş, “Kuantum Kodlar”, J. Inst. Sci. and Tech., vol. 10, no. 1, pp. 556–562, 2020, doi: 10.21597/jist.569915.
ISNAD Dertli, Abdullah - Çengellenmiş, Yasemin. “Kuantum Kodlar”. Journal of the Institute of Science and Technology 10/1 (March 2020), 556-562. https://doi.org/10.21597/jist.569915.
JAMA Dertli A, Çengellenmiş Y. Kuantum Kodlar. J. Inst. Sci. and Tech. 2020;10:556–562.
MLA Dertli, Abdullah and Yasemin Çengellenmiş. “Kuantum Kodlar”. Journal of the Institute of Science and Technology, vol. 10, no. 1, 2020, pp. 556-62, doi:10.21597/jist.569915.
Vancouver Dertli A, Çengellenmiş Y. Kuantum Kodlar. J. Inst. Sci. and Tech. 2020;10(1):556-62.