Abstract
In this paper, we study quantum codes over \(F_q\) from cyclic codes over \(F_q+uF_q+vF_q+uvF_q,\) where \(u^2=u,~v^2=v,~uv=vu,~q=p^m\), and p is an odd prime. We give the structure of cyclic codes over \(F_q+uF_q+vF_q+uvF_q\) and obtain self-orthogonal codes over \(F_q\) as Gray images of linear and cyclic codes over \(F_q+uF_q+vF_q+uvF_q\). In particular, we decompose a cyclic code over \(F_q+uF_q+vF_q+uvF_q\) into four cyclic codes over \(F_q\) to determine the parameters of the corresponding quantum code.
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The authors are thankful to the anonymous referees for their careful reading of the paper and valuable comments.
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Ashraf, M., Mohammad, G. Quantum codes from cyclic codes over \(F_q+uF_q+vF_q+uvF_q\) . Quantum Inf Process 15, 4089–4098 (2016). https://doi.org/10.1007/s11128-016-1379-8
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DOI: https://doi.org/10.1007/s11128-016-1379-8