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Pré-Publication, Document De Travail Année : 2023

Duality of codes over non-unital rings of order four

Résumé

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 E that coincides with the notion of quasi self-dual code introduced in (Alahmadi et al, 2022). We characterize selfdual 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 residue and torsion codes. A MacWilliams formula is established for linear codes over the non-commutative ring E.
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Dates et versions

hal-04040123 , version 1 (21-03-2023)
hal-04040123 , version 2 (25-03-2023)

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  • HAL Id : hal-04040123 , version 1

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Adel Alahmadi, Asmaa Melaibari, Patrick Solé. Duality of codes over non-unital rings of order four. 2023. ⟨hal-04040123v1⟩
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