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The Mass Formula for Self-Orthogonal and Self-Dual Codes over a Non-Unitary Non-Commutative Ring

Author

Listed:
  • Adel Alahmadi

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

  • Altaf Alshuhail

    (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 Hail, Hail 55431, 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

In this paper, we derive a mass formula for the self-orthogonal codes and self-dual codes over a non-commutative non-unitary ring, namely, E p = a , b | p a = p b = 0 , a 2 = a , b 2 = b , a b = a , b a = b , where a ≠ b and p is any odd prime. We also give a classification of self-orthogonal codes and self-dual codes over E p , where p = 3 , 5 , and 7, in short lengths.

Suggested Citation

  • Adel Alahmadi & Altaf Alshuhail & Rowena Alma Betty & Lucky Galvez & Patrick Solé, 2024. "The Mass Formula for Self-Orthogonal and Self-Dual Codes over a Non-Unitary Non-Commutative Ring," Mathematics, MDPI, vol. 12(6), pages 1-11, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:6:p:862-:d:1357552
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    References listed on IDEAS

    as
    1. Adel Alahmadi & Altaf Alshuhail & Rowena Alma Betty & Lucky Galvez & Patrick Solé, 2023. "Mass Formula for Self-Orthogonal and Self-Dual Codes over Non-Unital Rings of Order Four," Mathematics, MDPI, vol. 11(23), pages 1-17, November.
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