The build-up construction of quasi self-dual codes over a non-unital ring

Adel Alahmadi (1) , Alaa Altassan (1) , Hatoon Shoaib (1) , Amani Alkathiry (1) , Alexis Bonnecaze (2) , Patrick Solé (2)

1 King Abdulazziz University
2 I2M - Institut de Mathématiques de Marseille

We study a recursive construction of self-orthogonal codes over E. We classify, up to permutation equivalence, self-orthogonal codes of length n and size 2 n (called here quasi self-dual codes or QSD) up to the length n = 12. In particular, we classify Type IV codes (QSD codes with even weights) up to n = 12.

Mots clés: Non-unital rings; self-orthogonal codes; type IV codes.; Non-unital rings

Domaines: Théorie de l'information [cs.IT]

Adel Alahmadi, Alaa Altassan, Hatoon Shoaib, Amani Alkathiry, Alexis Bonnecaze, et al.. The build-up construction of quasi self-dual codes over a non-unital ring. Journal of Algebra and Its Applications, 2021, ⟨10.1142/S0219498822501432⟩. ⟨hal-03189828v2⟩