Abstract
In this paper, we study a class of skew constacyclic codes over the ring \(R=F_q+u_1F_{q}+\cdots +u_{2m}F_{q}\), where \(u_i^2=u_i\), \(u_iu_j=u_ju_i=0\), for \(i,j=1,2,\ldots ,2m ~,~ i \ne j\) and \(q=p^s\), and derive the generator polynomials of this class of codes over R. Also, by using Calderbank–Shor–Steane construction, some new non-binary quantum codes have been obtained. Moreover, new quantum codes \([[225, 201, 5]]_9\), \([[351, 333, 4]]_9\), \([[405, 393, 3]]_9\), \([[405, 381, 5]]_{9}\) have been constructed.
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Acknowledgements
The authors are thankful to the anonymous referees for their careful reading of the paper and valuable comments. The first author is thankful to the University Grant Commission (UGC), Govt. of India, for financial support under Sr. No. 2061441025 with Ref No. 22/06/2014(i)EU-V.
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Bag, T., Ashraf, M., Mohammad, G. et al. Quantum codes from \((1-2u_1-2u_2-\cdots -2u_m)\)-skew constacyclic codes over the ring \(F_q+u_1F_{q}+\cdots +u_{2m}F_{q}\). Quantum Inf Process 18, 270 (2019). https://doi.org/10.1007/s11128-019-2384-5
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DOI: https://doi.org/10.1007/s11128-019-2384-5