Duality of Codes over Non-unital Rings of Order Six

2025/02/25 by Altaf Alshuhail, Alshuhail, Altaf, Rowena Alma Betty +3 · 1 citation
Computer Science · Mathematics · #16D10 #94B05 #Advanced Topics in Algebra #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2502.18069

openalex publication_date 2025/02/25 · openalex created_date 2025/10/15 · openalex updated_date 2026/07/28

Abstract

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 C_a and a ternary code C_b. We characterize self-orthogonal, self-dual and quasi self-dual (QSD) codes over these rings using the codes C_a and 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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• Symplectic Quasi Self-dual, Self-dual, and LCD Codes over Non-unital Rings of Order Six

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