Type IV codes over a non-local non-unital ring

• 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. 963-978
• Idioma: inglés
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• Resumen

  • There is a local ring H of order 4, without identity for the multiplication, defined by generators and relations as H =?a, b | 2a = 2b = 0, a2 = 0, b2 = b, ab = ba = 0?.

    We classify self orthogonal codes of length n and size 2n (called here quasi self-dual codes or QSD) up to the length n = 6. In particular, we classify quasi Type IV codes (a subclass of Type IV codes, viz QSD codes with even weights) up to n = 6.