Duality of Codes over Non-unital Rings of Order Four
| Autor: | Adel Alahmadi, Asmaa Melaibari, Patrick Solé |
|---|---|
| Přispěvatelé: | King Abdul Aziz University (KAU), Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: |
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General Computer Science [MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC] General Engineering [MATH.MATH-IT]Mathematics [math]/Information Theory [math.IT] non-unitary rings additive codes two-Lee weight code one-Lee weight code Generator matrix Gray map linear code one-Lee weight code two-Lee weight code self-dual codes LCD codes General Materials Science linear code Electrical and Electronic Engineering Generator matrix |
| Zdroj: | IEEE Access IEEE Access, 2023, 30, pp.1-1. ⟨10.1109/ACCESS.2023.3261131⟩ |
| ISSN: | 2169-3536 |
| DOI: | 10.1109/ACCESS.2023.3261131⟩ |
| Popis: | International audience; In this paper, we present a basic theory of the duality of linear codes over three of the non-unital rings of order four; namely I, E , and H as denoted in (Fine, 1993). A new notion of duality is introduced in the case of the non-commutative ring E . The notion of self-dual codes with respect to this duality coincides with that of quasi self-dual codes over E as introduced in (Alahmadi et al , 2022). We characterize self-dual codes and LCD codes over the three rings, and investigate the properties of their corresponding additive codes over F 4 . We study the connection between the dual of any linear code over these rings and the dual of its associated binary codes. A MacWilliams formula is established for linear codes over E . |
| Databáze: | OpenAIRE |
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