Abstract
Let p be a prime of the form \(p=mt+1\), where integers \(t\ge 1, m\ge 2\) and \(R_m=\mathbb {F}_p[u]/\langle u^m-1\rangle .\) Thus, \(R_m\) is a finite commutative non-chain ring. For a given unit \(\lambda \in R_m\), we study \(\lambda \)-constacyclic codes of length n over \(R_m\). The necessary and sufficient conditions for these codes to contain their Euclidean duals are determined. As an application from dual-containing \(\lambda \)-constacyclic codes over \(R_m\), for \(m=2,3,4\), we obtain many new quantum codes that improve on the known existing quantum codes.
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Acknowledgements
The authors acknowledge the financial support provided by the NSTIP strategic technologies program in the Kingdom of Saudi Arabia—Project No (12-MAT3055-03), and extend the thanks to the Science and Technology Unit, King Abdulaziz University for their technical support. All authors would like to thank the Editor and anonymous referee(s) for careful reading and constructive suggestions to improve the presentation of the manuscript.
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Alahmadi, A., Islam, H., Prakash, O. et al. New quantum codes from constacyclic codes over a non-chain ring. Quantum Inf Process 20, 60 (2021). https://doi.org/10.1007/s11128-020-02977-y
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DOI: https://doi.org/10.1007/s11128-020-02977-y