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The Build-Up Construction for Codes over a Commutative Non-Unitary Ring of Order 9

Author

Listed:
  • Adel Alahmadi

    (Research Group of Algebraic Structures and Applications, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Tamador Alihia

    (Research Group of Algebraic Structures and Applications, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    Department of Mathematics, Faculty of Science, University of Qassim, Qassim 52373, Saudi Arabia)

  • Rowena Alma Betty

    (Institute of Mathematics, University of the Philippines Diliman, Quezon City 1101, Philippines)

  • Lucky Galvez

    (Institute of Mathematics, University of the Philippines Diliman, Quezon City 1101, Philippines)

  • Patrick Solé

    (I2M (CNRS, University of Aix-Marseille, Centrale Marseille), 13009 Marseilles, France)

Abstract

The build-up method is a powerful class of propagation rules that generate self-dual codes over finite fields and unitary rings. Recently, it was extended to non-unitary rings of order 4, to generate quasi self-dual codes. In the present paper, we introduce three such propagation rules to generate self-orthogonal, self-dual and quasi self-dual codes over a special non-unitary ring of order 9. As an application, we classify the three categories of codes completely in length at most 3, and partially in lengths 4 and 5, up to monomial equivalence.

Suggested Citation

  • Adel Alahmadi & Tamador Alihia & Rowena Alma Betty & Lucky Galvez & Patrick Solé, 2024. "The Build-Up Construction for Codes over a Commutative Non-Unitary Ring of Order 9," Mathematics, MDPI, vol. 12(6), pages 1-25, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:6:p:860-:d:1357517
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