Duality of codes over non-unital rings of order six
Altaf Alshuhail, Rowena Alma Betty, Lucky Galvez · AIMS Mathematics · 2025
Some basic theory on the duality of codes over two non-unital rings of order $ 6 $, namely $ H_{23} $ and $ H_{32} $ is presented. For a code $ {{\mathcal C}} $ over these rings, there is an associated binary code $ {{\mathcal C}}_a $ and a ternary code $ {{\mathcal C}}_b $. Self-orthogonal, self-dual, and quasi self-dual (QSD) codes over these rings are characterized using the associated codes $ {{\mathcal C}}_a $ and $ {{\mathcal C}}_b $, and a classification of self-orthogonal codes for short lengths is given. In addition, a building-up construction for self-orthogonal codes is presented, and cyclic and linear complementary dual (LCD) codes over the said rings are introduced.