The Build-Up Construction for Codes over a Commutative Non-Unitary Ring of Order 9
Adel Alahmadi,
Tamador Alihia,
Rowena Alma Betty,
Lucky Galvez,
Patrick Solé
Affiliations
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
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
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.
