We present some basic theory on the duality of codes over two non-unital rings of order 6, namely H₂₃ and H₃₂. For a code C over these rings, we associate a binary code Cₐ and a ternary code Cb. We characterize self-orthogonal, self-dual and quasi self-dual (QSD) codes over these rings using the codes Cₐ and Cb. In addition, we present a building-up construction for self-orthogonal codes, introduce cyclic codes and linear complementary dual (LCD) codes. We also gave a classification of self-orthogonal codes for short lengths.
Alshuhail et al. (Tue,) studied this question.
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