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New quantum codes from constacyclic codes over a non-chain ring

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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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Authors and Affiliations

  1. Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

    Adel Alahmadi, Ahmad Alkenani, Najat Muthana & Rola Hijazi

  2. Department of Mathematics, Indian Institute of Technology Patna, Patna, 801 106, India

    Habibul Islam & Om Prakash

  3. I2M, (CNRS, Aix-Marseille University, Centrale Marseille), Marseille, France

    Patrick Solé

  4. Research Group of Algebraic Structure and Its Applications, Deanship of Scientific Research, King Abdulaziz University, Jeddah, Saudi Arabia

    Adel Alahmadi

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  1. Adel Alahmadi
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  2. Habibul Islam
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  3. Om Prakash
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  4. Patrick Solé
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  5. Ahmad Alkenani
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  6. Najat Muthana
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  7. Rola Hijazi
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Correspondence to Adel Alahmadi.

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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

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