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arXiv · 2502.18069

Duality of Codes over Non-unital Rings of Order Six

Altaf Alshuhail·Rowena Alma Betty·Lucky Galvez
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Abstract

We present some basic theory on the duality of codes over two non-unital rings of order $6$, namely $H_{23}$ and $H_{32}$. For a code $\mathcal{C}$ over these rings, we associate a binary code $\mathcal{C}_a$ and a ternary code $\mathcal{C}_b$. We characterize self-orthogonal, self-dual and quasi self-dual (QSD) codes over these rings using the codes $\mathcal{C}_a$ and $\mathcal{C}_b$. 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.

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Altaf Alshuhail, Rowena Alma Betty, Lucky Galvez. 2025-02-25. Duality of Codes over Non-unital Rings of Order Six. https://arxiv.org/abs/2502.18069

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