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Quantum Codes

Yıl 2020, Cilt: 10 Sayı: 1, 556 - 562, 01.03.2020

Abdullah Dertli , Yasemin Çengellenmiş

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

Öz


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.

Anahtar Kelimeler

Qunatum codes Gray map cyclic codes

Kaynakça

  • 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

Yıl 2020, Cilt: 10 Sayı: 1, 556 - 562, 01.03.2020

Abdullah Dertli , Yasemin Çengellenmiş

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

Öz

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

Anahtar Kelimeler

Kuantum kodlar devirli kodlar Gray dönüşümü

Kaynakça

  • 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.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Matematik
Bölüm Matematik / Mathematics
Yazarlar

Abdullah Dertli 0000-0001-8687-032X

Yasemin Çengellenmiş Bu kişi benim 0000-0002-8133-9836

Yayımlanma Tarihi 1 Mart 2020
Gönderilme Tarihi 24 Mayıs 2019
Kabul Tarihi 8 Ekim 2019
Yayımlandığı Sayı Yıl 2020 Cilt: 10 Sayı: 1

Kaynak Göster

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. Iğdır Üniv. Fen Bil Enst. Der. Mart 2020;10(1):556-562. doi:10.21597/jist.569915
Chicago Dertli, Abdullah, ve Yasemin Çengellenmiş. “Kuantum Kodlar”. Journal of the Institute of Science and Technology 10, sy. 1 (Mart 2020): 556-62. https://doi.org/10.21597/jist.569915.
EndNote Dertli A, Çengellenmiş Y (01 Mart 2020) Kuantum Kodlar. Journal of the Institute of Science and Technology 10 1 556–562.
IEEE A. Dertli ve Y. Çengellenmiş, “Kuantum Kodlar”, Iğdır Üniv. Fen Bil Enst. Der., c. 10, sy. 1, ss. 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 (Mart 2020), 556-562. https://doi.org/10.21597/jist.569915.
JAMA Dertli A, Çengellenmiş Y. Kuantum Kodlar. Iğdır Üniv. Fen Bil Enst. Der. 2020;10:556–562.
MLA Dertli, Abdullah ve Yasemin Çengellenmiş. “Kuantum Kodlar”. Journal of the Institute of Science and Technology, c. 10, sy. 1, 2020, ss. 556-62, doi:10.21597/jist.569915.
Vancouver Dertli A, Çengellenmiş Y. Kuantum Kodlar. Iğdır Üniv. Fen Bil Enst. Der. 2020;10(1):556-62.
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