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

Adel Alahmadi (), Tamador Alihia, Rowena Alma Betty, Lucky Galvez and Patrick Solé
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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

Mathematics, 2024, vol. 12, issue 6, 1-25

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.

Keywords: non-unitary rings; self-dual codes; build-up construction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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