Quasi self-dual codes over non-unital rings of order six

• Alahmadi, Adel ^[1] ; Alkathiry, Amani ^[2] ; Altassan, Alaa ^[1] ; Basaffar, Widyan ^[1] ; Bonnecaze, Alexis ^[3] ; Shoaib, Hatoon ^[1] ; Solé, Patrick ^[3]
  1. [1] King Abdulaziz University

     King Abdulaziz University

     Arabia Saudí

     
  2. [2] Umm al-Qura University

     Umm al-Qura University

     Arabia Saudí

     
  3. [3] Aix-Marseille University

     Aix-Marseille University

     Arrondissement de Marseille, Francia

     

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• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 39, Nº. Extra 4, 2020 (Ejemplar dedicado a: Special Issue: Mathematical Computation in Combinatorics and Graph Theory; i), págs. 1083-1095
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-2020-04-0066
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• Resumen

  • There exist two semi-local rings of order 6 without identity for the multiplication. We classify up to coordinate permutation self-orthogonal codes of length n and size 6n/2 over these rings (called here quasi self-dual codes or QSD) till the length n = 8. To any such code is attached canonically a ?6-code, which, when self-dual, produces an unimodular lattice by Construction A.

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