Quantum codes from cyclic codes over \(F_q+uF_q+vF_q+uvF_q\)

1. Aly, S.A., Klappenecker, A., Sarvepalli, P.K.: On quantum and classical BCH codes. IEEE Trans. Inf. Theory 53, 1183–1188 (1995)

   Article  MathSciNet  MATH  Google Scholar 

2. Ashraf, M., Mohammad, G.: Quantum codes from cyclic codes over \(F_3+vF_3\). Int. J. Quantum Inf. 12(6), 1450042 (2014)

   Article  MathSciNet  MATH  Google Scholar 

3. Ashraf, M., Mohammad, G.: Construction of quantum codes from cyclic codes over \(F_p+vF_p\). Int. J. Inf. Coding Theory 3(2), 137–144 (2015)

   Article  MathSciNet  MATH  Google Scholar 

4. Calderbank, A.R., Rains, E.M., Shor, P.M., Sloane, N.J.A.: Quantum error-correction via codes over GF(4). IEEE Trans. Inf. Theory 44, 1369–1387 (1998)

   Article  MathSciNet  MATH  Google Scholar 

5. Dertli, A., Cengellenmis, Y., Eren, S.: On quantum codes obtained from cyclic codes over \(A_2\). Int. J. Quantum Inf. 13(3), 1550031 (2015)

   Article  MathSciNet  MATH  Google Scholar 

6. Feng, K., Ling, S., Xing, C.: Asymtotic bounds on quantum codes from algebraic geometry codes. IEEE Trans. Inf. Theory 52, 986–991 (2006)

   Article  MathSciNet  MATH  Google Scholar 

7. Grassl, M., Beth, T.: On optimal quantum codes. Int. J. Quantum Inf. 2, 55–64 (2004)

   Article  MATH  Google Scholar 

8. Gaurdia, G., Palazzo Jr., R.: Constructions of new families of nonbinary CSS codes. Discrete Math. 310, 2935–2945 (2010)

   Article  MathSciNet  MATH  Google Scholar 

9. Gottesman, D.: An introduction to quantum error-correction. Proc. Symp. Appl. Math. 68, 13–27 (2010)

   Article  MathSciNet  MATH  Google Scholar 

10. Ketkar, A., Klappenecker, A., Kumar, S., Sarvepalli, P.K.: Nonbinary quantum stabilizer codes over finite fields. IEEE Trans. Inf. Theory 52, 4892–4914 (2006)

    Article  MathSciNet  MATH  Google Scholar 

11. Kai, X., Zhu, S.: Quaternary construction of quantum codes from cyclic codes over \(F_4+uF_4\). Int. J. Quantum Inf. 9, 689–700 (2011)

    Article  MathSciNet  MATH  Google Scholar 

12. Li, R., Xu, Z., Li, X.: Binary construction of quantum codes of minimum distance three and four. IEEE Trans. Inf. Theory 50, 1331–1335 (2004)

    Article  MathSciNet  MATH  Google Scholar 

13. Li, R., Xu, Z.: Construction of \([[n, n-4, 3]]_q\) quantum codes for odd prime power \(q\). Phys. Rev. A 82, 1–4 (2010)

    Google Scholar 

14. Qian, J., Ma, W., Gou, W.: Quantum codes from cyclic codes over finite ring. Int. J. Quantum Inf. 7, 1277–1283 (2009)

    Article  MATH  Google Scholar 

15. Qian, J.: Quantum codes from cyclic codes over \(F_2+vF_2\). J. Inf. Comput. Sci. 10, 1715–1722 (2013)

    Article  Google Scholar 

16. Shor, P.W.: Scheme for reducing decoherence in quantum memory. Phys. Rev. A 52, 2493–2496 (1995)

    Article  ADS  Google Scholar 

17. Steane, A.M.: Simple quantum error-correcting codes. Phys. Rev. A 54, 4741–4751 (1996)

    Article  ADS  MathSciNet  MATH  Google Scholar 

18. Yao, T., Shi, M., Sole, P.: Skew cyclic codes over \(F_q+uF_q+vF_q+uvF_q\). J. Algebra Comb. Discrete Appl. 2(3), 163–168 (2015)

    MathSciNet  Google Scholar 

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