The build up construction for codes over a non-commutative non-unitary ring of order $ 9

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...

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Bibliographic Details
Published inAIMS mathematics Vol. 9; no. 7; pp. 18278 - 18307
Main Authors Alahmadi, Adel, Alihia, Tamador, Solé, Patrick
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2024
Subjects
build-up construction
Information Theory
Mathematics
non-unitary rings
self-dual codes
self-dual codes
non-unitary rings
build-up construction
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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2024892