Quantum Codes from (1-2w-2uv)-Constacyclic Codes over the F_q+uF_q+vF_q+wF_q+uvF_q

Year 2022, , 46 - 55, 27.03.2022

Ceremnur Tetik , Abdullah Dertli

https://doi.org/10.18185/erzifbed.911472

Abstract

In this paper, we give construction of quantum codes over F_q from (1-2w-2uv) - constacyclic codes over the F_q+uF_q+vF_q+wF_q+uvF_q, where u^2=u,v^2=v,w^2=w,uv=vu,uw=wu=vw=wv=0, q=p^m and p is an odd prime. We determine the parameters of quantum error correcting codes which constructed from (1-2w-2uv) - constacyclic codes over the F_q+uF_q+vF_q+wF_q+uvF_q.

Keywords

Quantum code, Constacyclic Code, Gray Map

References

• Calderbank, A. R., Rains, E. M., Shor, P. M. and Sloane, N. J. 1998. “Quantum Error Correction via Codes over GF(4)”, IEEE Transactions on Information Theory, 1369-1387.
• Gao, J. and Wang, Y. 2018. “u-Constacyclic Codes over F_p+uF_p and Their Applications of Constructing New Non-binary Quantum Codes”, Quantum Information Processing, 17(1), 1-9.
• Islam, H. and Prakash, O. 2020. “New Quantum Codes from Constacyclic and Additive Constacyclic Codes”, Quantum Information Processing, 19(9), 1-17.
• Li, J., Gao J. and Wang Y. 2018. “Quantum Codes from (1-2v)-Constacyclic Codes over F_q+uF_q+vF_q+uvF_q”, Discrete Math., 10(4), 1850046.
• Mohan, C. and Durairajan, C. 2020. “Skew-constacyclic codes over R”, Malaya Journal of Matematik, 8(4), 1502-1508.
• Shor, P. W. 1995. “Scheme for Reducing Decoherence in Quantum Memory”, Physical Review A, 52, 2493-2496.