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

Adel Alahmadi (1) , Tamador Alihia (1) , Rowena Alma Betty (2) , Lucky Galvez (2) , Patrick Solé (3)

1 KAU - King Abdul Aziz University
2 UP System - University of the Philippines
3 I2M - Institut de Mathématiques de Marseille

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.

Mots clés: non-unitary rings; self-dual codes; build-up construction

Domaines: Théorie de l'information et codage [math.IT]

Adel Alahmadi, Tamador Alihia, Rowena Alma Betty, Lucky Galvez, Patrick Solé. The Build-Up Construction for Codes over a Commutative Non-Unitary Ring of Order 9. Mathematics , 2024, ⟨10.3390/math12060860⟩. ⟨hal-04505915⟩