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 four to generate quasi self-dual codes. In the present paper we introduce three such propagation rules to generate self-orthogonal, one-sided self-dual, and self-dual codes over a special non-unitary ring of order 9. As an application, we classify the three categories of codes in lengths at most $ 7, $ up to monomial equivalence. Mass formulas for the three classes of codes considered ensure that the classification is complete.
Citation: Adel Alahmadi, Tamador Alihia, Patrick Solé. The build up construction for codes over a non-commutative non-unitary ring of order $ 9 $[J]. AIMS Mathematics, 2024, 9(7): 18278-18307. doi: 10.3934/math.2024892
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 four to generate quasi self-dual codes. In the present paper we introduce three such propagation rules to generate self-orthogonal, one-sided self-dual, and self-dual codes over a special non-unitary ring of order 9. As an application, we classify the three categories of codes in lengths at most $ 7, $ up to monomial equivalence. Mass formulas for the three classes of codes considered ensure that the classification is complete.
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Adel Alahmadi, Tamador Alihia, Patrick Solé. The build up construction for codes over a non-commutative non-unitary ring of order $ 9 $[J]. AIMS Mathematics, 2024, 9(7): 18278-18307. doi: 10.3934/math.2024892
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